sin((1/2) cos-1 (4/5)) is equal to:

Question

sin((1/2) cos-1 (4/5)) is equal to: (A)  - (1/√10)  (B)  (1/√10)  (C)  - (1/10) (D) (1/10)

Tardigrade Admin · Accepted Answer

Given: sin ( (1/2) cos-1 (4/5)) Now, Let (4/5) = cos 2 θ ∴ sin ( (1/2) cos-1 (4/5) ) = sin((1/2) cos-1 cos 2 θ ) = sin( (1/2) ×2 θ) = sinθ = √(1- cos2θ/2) = √(1- (4/5)/2) = (1/√10)

Q. $sin (\frac{1}{2} cos^{- 1} \frac{4}{5})$ is equal to:

$- \frac{1}{10}$

$\frac{1}{10}$

$- \frac{1}{10}$

$\frac{1}{10}$

Given: $sin (\frac{1}{2} cos^{- 1} \frac{4}{5})$
Now, Let $\frac{4}{5} = cos 2 θ$
$∴ sin (\frac{1}{2} cos^{- 1} \frac{4}{5}) = sin (\frac{1}{2} cos^{- 1} cos 2 θ)$
$= sin (\frac{1}{2} \times 2 θ) = sin θ = \frac{1 - c o s 2 θ}{2}$
$= \frac{1 - \frac{4}{5}}{2} = \frac{1}{10}$

Q. sin(21​cos−154​) is equal to:

−10​1​

10​1​

−101​

101​

Given: sin(21​cos−154​) Now, Let 54​=cos2θ ∴sin(21​cos−154​)=sin(21​cos−1cos2θ) =sin(21​×2θ)=sinθ=21−cos2θ​​ =21−54​​​=10​1​

Q. $sin (\frac{1}{2} cos^{- 1} \frac{4}{5})$ is equal to:

$- \frac{1}{10}$

$\frac{1}{10}$

$- \frac{1}{10}$

$\frac{1}{10}$

Given: $sin (\frac{1}{2} cos^{- 1} \frac{4}{5})$
Now, Let $\frac{4}{5} = cos 2 θ$
$∴ sin (\frac{1}{2} cos^{- 1} \frac{4}{5}) = sin (\frac{1}{2} cos^{- 1} cos 2 θ)$
$= sin (\frac{1}{2} \times 2 θ) = sin θ = \frac{1 - c o s 2 θ}{2}$
$= \frac{1 - \frac{4}{5}}{2} = \frac{1}{10}$