Question

Let sintheta =2times square root 3/5 and pi/2

Answer 1

Given:

`sin\theta=(2√(3))/(5),\text{ and }(\pi)/(2)<\theta<\pi`

It's required to find cos 2θ.

We use the formula:

`cos(2\theta)=1-2sin^2\theta`

Substituting:

`cos(2\theta)=1-2((2√(3))/(5))^2`

Operating:

`\begin{gathered} cos(2\theta)=1-2*(4*3)/(25) \\ cos(2\theta)=1-(24)/(25) \\ cos(2\theta)=(1)/(25) \end{gathered}`

Answer: 1/25