Question

If $\sin \theta =\cos \theta$, $0⩽\theta ⩽{90}^{\circ }$
$\left(a\right){30}^{\circ }$
$\left(b\right){45}^{\circ }$
$\left(c\right){60}^{\circ }$
$\left(d\right){90}^{\circ }$

Answer 1

Given:

$\sin \theta =\cos \theta$, $(0^{\circ }⩽\theta ⩽{90}^{\circ })$

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

$\Rightarrow \tan \theta =1$ [ $\because$ $\frac{\sin \theta }{\cos \theta }=\tan \theta$]

$\Rightarrow \tan \theta =\tan {45}^{\circ }$ [$\because \tan {45}^{\circ }=1$]

$\Rightarrow \theta ={45}^{\circ }$

Hence, Option $\left(b\right)$ is correct.