Question

if sin theta = cos (theta -45 )theta &(theta - 45) are acute angle find the value of theta?

Answer 1

Sin (theta) = cos (theta -45)

so, Cos (90-theta) = cos (theta -45)       [Cos(90-A) = SinA]
 Hence, 90 - theta = theta - 45
           so, theta = 135/2 = 67.5°

Answer 2

Answer:

The value of theta $(\theta)$ is 67.5°

Step-by-step explanation:

We are given an equation,

$\sin\theta=\cos(\theta-45^{\circ})$

where, $\theta$ and $(\theta-45^{\circ})$ are acute angle.

using formula, $\sin\theta = \cos(90^{\circ}-\theta)$

$\cos(90^{\circ}-\theta)=\cos(\theta-45^{\circ})$

$90^{\circ}-\theta=\theta-45^{\circ}$

$2\theta=90^{\circ}+45^{\circ}$

$\theta=\frac{135^{\circ}}{2}=67.5^{\circ}$

Thus, The value of theta $(\theta)$ is 67.5°