Question

Find the value of cos2 theta if 2 sin2 theta = root 3

Answer 1

2sin²θ=√3
or, sin²θ=√3/2
sin²θ+cos²θ=1
or, cos²θ=1-sin²θ
or, cos²θ=1-√3/2
or, cos²θ=(2-√3)/2

Answer 2

Answer:

$\frac{2-\sqrt{3}}{2}=cos^2 \theta$

Step-by-step explanation:

Given : $2 sin^2 \theta = \sqrt{3}$

To Find : Value of $cos^2\theta$

Solution :

$2 sin^2 \theta = \sqrt{3}$

$sin^2 \theta = \frac{\sqrt{3}}{2}$

Identity : $Sin^2 \theta +cos^2 \theta = 1$

$1-cos^2 \theta = \frac{\sqrt{3}}{2}$

$1- \frac{\sqrt{3}}{2}=cos^2 \theta$

$\frac{2-\sqrt{3}}{2}=cos^2 \theta$

Hence $\frac{2-\sqrt{3}}{2}=cos^2 \theta$