Question

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

Answer 1

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

so, cos ($90-\theta$) =cos $(\theta -{45}^o)$ [cos(90-A) = sinA]
Hence, $90-\theta$ = $\theta -{45}^o$ [Since angles are same]

so, $\theta$ = $\frac{135}{2}$ = 67.5°