Advertisements
Advertisements
Question
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Advertisements
Solution
We know that
\[\sin^{- 1} \left( \sin{x} \right) = x\]
We have
\[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right) = \sin^{- 1} \left\{ \sin\left( \pi - \frac{3\pi}{5} \right) \right\} \left[ \because \left( \pi - \frac{3\pi}{5} \right) \in \left[ - \frac{\pi}{2}, \frac{\pi}{2} \right] \right]\]
\[ = \sin^{- 1} \left( \sin\frac{2\pi}{5} \right)\]
\[ = \frac{2\pi}{5}\]
∴ \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right) = \frac{2\pi}{5}\]
APPEARS IN
RELATED QUESTIONS
If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`sec^-1(sec (5pi)/4)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`cot^-1(cot pi/3)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Evaluate the following:
`sin(cos^-1 5/13)`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`cot(tan^-1a+cot^-1a)`
If `cot(cos^-1 3/5+sin^-1x)=0`, find the values of x.
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
`5tan^-1x+3cot^-1x=2x`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Write the value of cos−1 (cos 1540°).
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value of sin−1 (sin 1550°).
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value of cos−1 (cos 6).
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Write the principal value of `sin^-1(-1/2)`
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
If tan−1 (cot θ) = 2 θ, then θ =
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
