Question

If $\sin x=\cos x$ and $x$ is acute, state the value of $x$.

Answer 1

$\sin x=\cos x$

$\Rightarrow \frac{\sin x}{\cos x}=1$

$\Rightarrow \tan \left(x\right)=1$

$\Rightarrow x={\tan }^{-1}\left(1\right)$

$\Rightarrow x={45}^o$

(or)

$\sin x=\cos x$

$\Rightarrow \sin x=\sin (90-x)$

$\Rightarrow x={\sin }^{-1}\left[\sin \right(90-x\left)\right]$

$\Rightarrow x=90-x$

$\Rightarrow 2x=90$

$\Rightarrow x=\frac{90}{2}$

$\Rightarrow x={45}^o$.