Question

If $\cot 2\theta =\sqrt{3}$ and $\theta$ is acute angle, then ${\sin }^2(45+\theta )-{\cos }^2(75-\theta )$ is

• A. 1
• B. $\frac{\sqrt{3}-1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{\sqrt{3}-2}{4}$

Answer 1

The correct option is C $\frac{1}{2}$

$cot2\theta =\sqrt{3}=cot{30}^o\Rightarrow \theta =15$
$si{n}^2(45+15)-co{s}^2(75-15)=si{n}^{2}60-co{s}^{2}60=\frac{1}{2}$