Advertisements
Advertisements
प्रश्न
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
Advertisements
उत्तर
\[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\} = \sin^{- 1} \left\{ \cos\left[ \sin^{- 1} \left( \sin\frac{\pi}{3} \right) \right] \right\}\]
\[ = \sin^{- 1} \left[ \cos\left( \frac{\pi}{3} \right) \right]\]
\[ = \sin^{- 1} \left[ \frac{1}{2} \right]\]
\[ = \sin^{- 1} \left[ \sin\left( \frac{\pi}{3} \right) \right]\]
\[ = \frac{\pi}{3}\]
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
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`
`sin^-1{(sin - (17pi)/8)}`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Evaluate the following:
`\text(cosec)^-1(\text{cosec} pi/4)`
Evaluate the following:
`cot^-1(cot pi/3)`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`tan{cos^-1(-7/25)}`
Evaluate:
`cos(tan^-1 3/4)`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
`sin(sin^-1 1/5+cos^-1x)=1`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the range of tan−1 x.
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
If tan−1 3 + tan−1 x = tan−1 8, then x =
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
