Question

$\sqrt{3}\tan 2\theta =\cos 0^{\circ }+\sin {45}^{\circ }-\cos {45}^{\circ }then\theta is$

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is D ${15}^{\circ }$

$\sqrt{3}\tan 2\theta =\cos 0^{\circ }+\sin {45}^{\circ }-\cos {45}^{\circ }\Rightarrow \sqrt{3}\tan 2\theta =1+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}=1\Rightarrow \tan 2\theta =\frac{1}{\sqrt{3}}\Rightarrow 2\theta ={30}^o\Rightarrow \theta ={15}^o$

Therefore, Answer is $\theta ={15}^o$