Question

If $sin3\theta =cos(\theta -{26}^{\circ }$), where $3\theta$ and $(\theta$-${26}^{\circ })$ are acute angles, then find the value of $\theta$.

Answer 1

$\Rightarrow sin3\theta =cos(\theta -{26}^{\circ }$)

$\Rightarrow sin3\theta =sin[{90}^{\circ }-(\theta -{26}^{\circ }\left)\right]$

$\Rightarrow 3\theta ={90}^{\circ }-\theta +{26}^{\circ }$

$\Rightarrow \theta =\frac{{116}^{\circ }}{4}$


$\Rightarrow \theta$ = ${29}^{\circ }$