Question

If sin $\theta$ = cos $(\theta -{45}^o)$, where $\theta$ is acute, find the value of $\theta$.

Answer 1

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

so, $cos(90-\theta )=cos(\theta -45)$ [Cos(90-A) = SinA]

Hence, on comparing

$90-\theta =\theta -45$

$2\theta =135$

$\theta =\frac{138}{2}=67.5$