Question

If $\theta$ and $(2\theta -45)$ are acute angles and $\sin \theta =\cos (2\theta -45)$, then $\tan \theta =.......$

• A. $1$
• B. $-1$
• C. $\sqrt{3}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is A $1$

$\theta +2\theta -{45}^{\circ }={90}^{\circ }$
$3\theta ={135}^{\circ }$
$\theta ={45}^{\circ }=\angle A$

$\angle C=2\theta -{45}^{\circ }$
$=(2\times 45)-{45}^{\circ }$
$={90}^{\circ }-{45}^{\circ }={45}^{\circ }$

Side opposite to equal angles are equal $\angle A=\angle C$

So, $BC=AB$

So, $\tan \theta =\frac{BC}{AB}=1$

So $1$ is correct.