Question

If $\sin 3\mathrm{A}=\cos \left(\mathrm{A}-26°\right)$, where $3\mathrm{A}$ is an acute angle, find the value of $A$.

Answer 1

Evaluating the given expression:

$\sin 3\mathrm{A}=\cos \left(\mathrm{A}-26°\right)$

$\cos (90°-3A)=\cos \left(\mathrm{A}-26°\right)\left[\because \cos (90°-A)=\sin A\right]$

$\Rightarrow$ $90°-3A=\mathrm{A}-26°$

$\Rightarrow$ $4A=116°$

$\Rightarrow$ $A=\frac{116}{4}$

$\Rightarrow$ $A=29°$

Hence, the value of the given expression is $29°$.