Question

if 2 (cos²θ - sin²θ) = 1 (θ is a positive acute angle ) , then cot θ equal to -

Answer 1

cos^2 x - sin^2 x = cos 2x = 1/2
2x = 60
cot x = √3

Answer 2

Answer:

The value of $\cot\theta =\sqrt 3$

Step-by-step explanation:

Given : $2(\cos^2 \theta-\sin^2 \theta)=1$ where, θ is a positive acute angle.

To find : The value of $\cot\theta$ ?

Solution :

Expression  $2(\cos^2 \theta-\sin^2 \theta)=1$

We know that,

$\cos 2\theta=\cos^2 \theta-\sin^2 \theta$

Substitute in the expression,

$2(\cos 2\theta)=1$

$\cos 2\theta=\frac{1}{2}$

$\cos 2\theta=\cos (60)$

$2\theta=60$

$\theta=30$

$\theta=\frac{\pi}{6}$

Now, we substitute the θ value in the cot θ.

$=\cot(30)$

$=\sqrt 3$

Therefore, The value of $\cot\theta =\sqrt 3$