Advertisements
Advertisements
प्रश्न
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Advertisements
उत्तर
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
संबंधित प्रश्न
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Find the domain of `f(x)=cos^-1x+cosx.`
`sin^-1(sin4)`
`sin^-1(sin2)`
Evaluate the following:
`tan^-1(tan2)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cot^-1(cot pi/3)`
Evaluate the following:
`sec(sin^-1 12/13)`
Evaluate the following:
`cos(tan^-1 24/7)`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
If `cot(cos^-1 3/5+sin^-1x)=0`, find the values of x.
`sin(sin^-1 1/5+cos^-1x)=1`
`5tan^-1x+3cot^-1x=2x`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
Solve the following equation for x:
`tan^-1 x/2+tan^-1 x/3=pi/4, 0<x<sqrt6`
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the principal value of `sin^-1(-1/2)`
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
If \[\cos^{- 1} x > \sin^{- 1} x\], then
If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
