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)`
`sin^-1(sin (5pi)/6)`
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`tan^-1(tan12)`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
`sin(sin^-1 1/5+cos^-1x)=1`
Solve the following equation for x:
`tan^-1 2x+tan^-1 3x = npi+(3pi)/4`
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)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`tan^-1 2/3=1/2tan^-1 12/5`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
Write the value of sin (cot−1 x).
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
The value of sin `["cos"^-1 (7/25)]` is ____________.
