Advertisements
Advertisements
प्रश्न
If θ = sin−1 {sin (−600°)}, then one of the possible values of θ is
विकल्प
`pi/3`
`pi/2`
`(2pi)/3`
`-(2pi)/3`
उत्तर
(a) `pi/3`
We know
\[\sin^{- 1} \left( \sin{x} \right) = x\]
Now,
\[\theta = \sin^{- 1} \left\{ \sin\left( - {600}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {720}^\circ - {600}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {120}^\circ \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( {180}^\circ - {120}^\circ \right) \right\} \left[ \because \sin{x} = \sin\left( \pi - x \right) \right]\]
\[ = \sin^{- 1} \left( \sin {60}^\circ \right)\]
\[ = {60}^\circ\]
APPEARS IN
संबंधित प्रश्न
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin pi/6)`
`sin^-1(sin (7pi)/6)`
`sin^-1(sin (5pi)/6)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`tan^-1(tan4)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate:
`cos(tan^-1 3/4)`
Solve the following equation for x:
`tan^-1 x/2+tan^-1 x/3=pi/4, 0<x<sqrt6`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
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 \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
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 =
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
If α = \[\tan^{- 1} \left( \frac{\sqrt{3}x}{2y - x} \right), \beta = \tan^{- 1} \left( \frac{2x - y}{\sqrt{3}y} \right),\]
then α − β =
If tan−1 3 + tan−1 x = tan−1 8, then x =
If 4 cos−1 x + sin−1 x = π, then the value of x is
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
Find the domain of `sec^(-1) x-tan^(-1)x`
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
The period of the function f(x) = tan3x is ____________.
