Advertisements
Advertisements
प्रश्न
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
उत्तर
\[\text{Let }y = \cos^{- 1} \left( \frac{3}{5} \right)\]
\[ \Rightarrow \cos{y} = \frac{3}{5}\]
Now,
\[\cos^2 \left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right) = \cos^2 \left( \frac{1}{2}y \right)\]
\[ = \frac{\cos{y} + 1}{2} \left[ \because \cos2x = 2 \cos^2 x - 1 \right]\]
\[ = \frac{\frac{3}{5} + 1}{2}\]
\[ = \frac{\frac{8}{5}}{2}\]
\[ = \frac{4}{5}\]
∴ \[\cos^2 \left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right) = \frac{4}{5}\]
APPEARS IN
संबंधित प्रश्न
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the domain of `f(x)=cos^-1x+cosx.`
`sin^-1(sin pi/6)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate:
`cos(tan^-1 3/4)`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
`tan^-1x+2cot^-1x=(2x)/3`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Solve the following equation for x:
`tan^-1 x/2+tan^-1 x/3=pi/4, 0<x<sqrt6`
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`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of cos−1 (cos 1540°).
Write the value of sin−1 (sin 1550°).
Write the value of cos−1 (cos 6).
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
