Advertisements
Advertisements
प्रश्न
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Advertisements
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
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
`sin^-1(sin (13pi)/7)`
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Evaluate the following:
`sin(cos^-1 5/13)`
Evaluate the following:
`sin(tan^-1 24/7)`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
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-4))+tan^-1((x+2)/(x+4))=pi/4`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
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 \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
tanx is periodic with period ____________.
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
