Express $x$ in terms of $a$ and $b$: $sin^-1 frac2a1+a^2 + sin^-1frac2b1+b^2 = 2tan^-1x$
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Find the value of $x$ from the following equation in terms of $a$ and $b$
$$sin^-1 2aover1+a^2 + sin^-12bover1+b^2 = 2tan^-1x$$
I tried to expand the LHS using the formula $$sin^-1c+sin^-1d = sin^-1left(csqrt1+d^2 + dsqrt1+c^2right)$$
But it didn't work out. Could anyone help me out?
trigonometry
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up vote
1
down vote
favorite
Find the value of $x$ from the following equation in terms of $a$ and $b$
$$sin^-1 2aover1+a^2 + sin^-12bover1+b^2 = 2tan^-1x$$
I tried to expand the LHS using the formula $$sin^-1c+sin^-1d = sin^-1left(csqrt1+d^2 + dsqrt1+c^2right)$$
But it didn't work out. Could anyone help me out?
trigonometry
I think you left out the parentheses on the right-hand side of the last formula. Please check that you agree with my edit.
â saulspatz
Sep 8 at 13:00
@saulspatz Oh yes. Thanks mate
â S.Nep
Sep 8 at 13:14
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Find the value of $x$ from the following equation in terms of $a$ and $b$
$$sin^-1 2aover1+a^2 + sin^-12bover1+b^2 = 2tan^-1x$$
I tried to expand the LHS using the formula $$sin^-1c+sin^-1d = sin^-1left(csqrt1+d^2 + dsqrt1+c^2right)$$
But it didn't work out. Could anyone help me out?
trigonometry
Find the value of $x$ from the following equation in terms of $a$ and $b$
$$sin^-1 2aover1+a^2 + sin^-12bover1+b^2 = 2tan^-1x$$
I tried to expand the LHS using the formula $$sin^-1c+sin^-1d = sin^-1left(csqrt1+d^2 + dsqrt1+c^2right)$$
But it didn't work out. Could anyone help me out?
trigonometry
trigonometry
edited Sep 8 at 17:54
Blue
44.4k868142
44.4k868142
asked Sep 8 at 12:50
S.Nep
394
394
I think you left out the parentheses on the right-hand side of the last formula. Please check that you agree with my edit.
â saulspatz
Sep 8 at 13:00
@saulspatz Oh yes. Thanks mate
â S.Nep
Sep 8 at 13:14
add a comment |Â
I think you left out the parentheses on the right-hand side of the last formula. Please check that you agree with my edit.
â saulspatz
Sep 8 at 13:00
@saulspatz Oh yes. Thanks mate
â S.Nep
Sep 8 at 13:14
I think you left out the parentheses on the right-hand side of the last formula. Please check that you agree with my edit.
â saulspatz
Sep 8 at 13:00
I think you left out the parentheses on the right-hand side of the last formula. Please check that you agree with my edit.
â saulspatz
Sep 8 at 13:00
@saulspatz Oh yes. Thanks mate
â S.Nep
Sep 8 at 13:14
@saulspatz Oh yes. Thanks mate
â S.Nep
Sep 8 at 13:14
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
3
down vote
Divide both sides by $2$, then using the $arctan(x)=y implies x=tan(y)$ you will get that $$x=tanleft(fracarcsinleft(frac2a1+a^2right)+arcsinleft(frac2b1+b^2right)2right)$$
Welcome to MSE. Your formatting will look a lot nicer if you usearctan
andtan
instead oftan
andarctan
.
â saulspatz
Sep 8 at 13:02
@saulspatz thank you!
â Donna Caligine
Sep 8 at 13:03
My pleasure. I also suggest that you put all mathematical expressions, including numbers, inside dollars signs.$2$
comes out as $2$.
â saulspatz
Sep 8 at 13:09
Welcome! Another typesetting hint: useleft( ... right)
instead of just( ... )
for parentheses that need to contain large expressions; they will grow as needed.
â Théophile
Sep 8 at 13:11
Now I'm one of you guys hahaha, thank you again for the great suggestions!
â Donna Caligine
Sep 8 at 13:16
 |Â
show 1 more comment
up vote
0
down vote
Let $arctan a=u,a=tan u$
If $-dfracpi2le2uledfracpi2iff -1le ale1$ $$P=arcsindfrac2a1+a^2=2arctan a$$
If $2u>dfracpi2,P=pi-2arctan a$
If $2u<-dfracpi2,P=-pi-2arctan a$
Now use my answer in showing $arctan(frac23) = frac12 arctan(frac125)$
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
Divide both sides by $2$, then using the $arctan(x)=y implies x=tan(y)$ you will get that $$x=tanleft(fracarcsinleft(frac2a1+a^2right)+arcsinleft(frac2b1+b^2right)2right)$$
Welcome to MSE. Your formatting will look a lot nicer if you usearctan
andtan
instead oftan
andarctan
.
â saulspatz
Sep 8 at 13:02
@saulspatz thank you!
â Donna Caligine
Sep 8 at 13:03
My pleasure. I also suggest that you put all mathematical expressions, including numbers, inside dollars signs.$2$
comes out as $2$.
â saulspatz
Sep 8 at 13:09
Welcome! Another typesetting hint: useleft( ... right)
instead of just( ... )
for parentheses that need to contain large expressions; they will grow as needed.
â Théophile
Sep 8 at 13:11
Now I'm one of you guys hahaha, thank you again for the great suggestions!
â Donna Caligine
Sep 8 at 13:16
 |Â
show 1 more comment
up vote
3
down vote
Divide both sides by $2$, then using the $arctan(x)=y implies x=tan(y)$ you will get that $$x=tanleft(fracarcsinleft(frac2a1+a^2right)+arcsinleft(frac2b1+b^2right)2right)$$
Welcome to MSE. Your formatting will look a lot nicer if you usearctan
andtan
instead oftan
andarctan
.
â saulspatz
Sep 8 at 13:02
@saulspatz thank you!
â Donna Caligine
Sep 8 at 13:03
My pleasure. I also suggest that you put all mathematical expressions, including numbers, inside dollars signs.$2$
comes out as $2$.
â saulspatz
Sep 8 at 13:09
Welcome! Another typesetting hint: useleft( ... right)
instead of just( ... )
for parentheses that need to contain large expressions; they will grow as needed.
â Théophile
Sep 8 at 13:11
Now I'm one of you guys hahaha, thank you again for the great suggestions!
â Donna Caligine
Sep 8 at 13:16
 |Â
show 1 more comment
up vote
3
down vote
up vote
3
down vote
Divide both sides by $2$, then using the $arctan(x)=y implies x=tan(y)$ you will get that $$x=tanleft(fracarcsinleft(frac2a1+a^2right)+arcsinleft(frac2b1+b^2right)2right)$$
Divide both sides by $2$, then using the $arctan(x)=y implies x=tan(y)$ you will get that $$x=tanleft(fracarcsinleft(frac2a1+a^2right)+arcsinleft(frac2b1+b^2right)2right)$$
edited Sep 8 at 13:13
Larry
31814
31814
answered Sep 8 at 12:57
Donna Caligine
356
356
Welcome to MSE. Your formatting will look a lot nicer if you usearctan
andtan
instead oftan
andarctan
.
â saulspatz
Sep 8 at 13:02
@saulspatz thank you!
â Donna Caligine
Sep 8 at 13:03
My pleasure. I also suggest that you put all mathematical expressions, including numbers, inside dollars signs.$2$
comes out as $2$.
â saulspatz
Sep 8 at 13:09
Welcome! Another typesetting hint: useleft( ... right)
instead of just( ... )
for parentheses that need to contain large expressions; they will grow as needed.
â Théophile
Sep 8 at 13:11
Now I'm one of you guys hahaha, thank you again for the great suggestions!
â Donna Caligine
Sep 8 at 13:16
 |Â
show 1 more comment
Welcome to MSE. Your formatting will look a lot nicer if you usearctan
andtan
instead oftan
andarctan
.
â saulspatz
Sep 8 at 13:02
@saulspatz thank you!
â Donna Caligine
Sep 8 at 13:03
My pleasure. I also suggest that you put all mathematical expressions, including numbers, inside dollars signs.$2$
comes out as $2$.
â saulspatz
Sep 8 at 13:09
Welcome! Another typesetting hint: useleft( ... right)
instead of just( ... )
for parentheses that need to contain large expressions; they will grow as needed.
â Théophile
Sep 8 at 13:11
Now I'm one of you guys hahaha, thank you again for the great suggestions!
â Donna Caligine
Sep 8 at 13:16
Welcome to MSE. Your formatting will look a lot nicer if you use
arctan
and tan
instead of tan
and arctan
.â saulspatz
Sep 8 at 13:02
Welcome to MSE. Your formatting will look a lot nicer if you use
arctan
and tan
instead of tan
and arctan
.â saulspatz
Sep 8 at 13:02
@saulspatz thank you!
â Donna Caligine
Sep 8 at 13:03
@saulspatz thank you!
â Donna Caligine
Sep 8 at 13:03
My pleasure. I also suggest that you put all mathematical expressions, including numbers, inside dollars signs.
$2$
comes out as $2$.â saulspatz
Sep 8 at 13:09
My pleasure. I also suggest that you put all mathematical expressions, including numbers, inside dollars signs.
$2$
comes out as $2$.â saulspatz
Sep 8 at 13:09
Welcome! Another typesetting hint: use
left( ... right)
instead of just ( ... )
for parentheses that need to contain large expressions; they will grow as needed.â Théophile
Sep 8 at 13:11
Welcome! Another typesetting hint: use
left( ... right)
instead of just ( ... )
for parentheses that need to contain large expressions; they will grow as needed.â Théophile
Sep 8 at 13:11
Now I'm one of you guys hahaha, thank you again for the great suggestions!
â Donna Caligine
Sep 8 at 13:16
Now I'm one of you guys hahaha, thank you again for the great suggestions!
â Donna Caligine
Sep 8 at 13:16
 |Â
show 1 more comment
up vote
0
down vote
Let $arctan a=u,a=tan u$
If $-dfracpi2le2uledfracpi2iff -1le ale1$ $$P=arcsindfrac2a1+a^2=2arctan a$$
If $2u>dfracpi2,P=pi-2arctan a$
If $2u<-dfracpi2,P=-pi-2arctan a$
Now use my answer in showing $arctan(frac23) = frac12 arctan(frac125)$
add a comment |Â
up vote
0
down vote
Let $arctan a=u,a=tan u$
If $-dfracpi2le2uledfracpi2iff -1le ale1$ $$P=arcsindfrac2a1+a^2=2arctan a$$
If $2u>dfracpi2,P=pi-2arctan a$
If $2u<-dfracpi2,P=-pi-2arctan a$
Now use my answer in showing $arctan(frac23) = frac12 arctan(frac125)$
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Let $arctan a=u,a=tan u$
If $-dfracpi2le2uledfracpi2iff -1le ale1$ $$P=arcsindfrac2a1+a^2=2arctan a$$
If $2u>dfracpi2,P=pi-2arctan a$
If $2u<-dfracpi2,P=-pi-2arctan a$
Now use my answer in showing $arctan(frac23) = frac12 arctan(frac125)$
Let $arctan a=u,a=tan u$
If $-dfracpi2le2uledfracpi2iff -1le ale1$ $$P=arcsindfrac2a1+a^2=2arctan a$$
If $2u>dfracpi2,P=pi-2arctan a$
If $2u<-dfracpi2,P=-pi-2arctan a$
Now use my answer in showing $arctan(frac23) = frac12 arctan(frac125)$
answered Sep 8 at 13:59
lab bhattacharjee
216k14153266
216k14153266
add a comment |Â
add a comment |Â
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I think you left out the parentheses on the right-hand side of the last formula. Please check that you agree with my edit.
â saulspatz
Sep 8 at 13:00
@saulspatz Oh yes. Thanks mate
â S.Nep
Sep 8 at 13:14