Question

If $\cos A=\sin \left(A-15\right)$, find $A$.

Answer 1

$\cos A=\sin (A-15)$

$\Rightarrow \sin (90-A)=\sin (A-15)$

$\Rightarrow 90-A=A-15$

$\Rightarrow -2A=-15-90=-105$

$\Rightarrow A=\frac{{105}^{\circ }}{2}=52{\frac{1}{2}}^{\circ }={52}^{\circ }{30}^{\prime }$