Question

If $\sin$ $\theta =\cos (\theta -{45}^{\circ }),$ where $\theta$ and $\theta -{45}^{\circ }$ are acute angles, find the degree measure of $\theta$.

Answer 1

Given ,

$\sin \theta =\cos (\theta -{45}^{\circ }),$ where $\theta$ and $\theta -{45}^{\circ }$ are acute angles

We know that,

$\sin \theta =\cos (90-\theta )$

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

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

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

$2\theta ={90}^{\circ }+{45}^{\circ }={135}^{\circ }$

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

$\theta =62\frac{1^{\circ }}{2}$