Question

The value of ${\sin }^2{60}^{\circ }.{\cos }^2{30}^{\circ }+\tan {45}^{\circ }.\cos {60}^{\circ }\sin {30}^{\circ }$ is

• A. $\frac{13}{16}$
• B. 5
• C. 1
• D. $-\frac{1}{2}$

Answer 1

Answer: (A)

$\frac{13}{16}$

${\sin }^2{60}^{\circ }.{\cos }^2{30}^{\circ }+\tan {45}^{\circ }.\cos {60}^{\circ }\sin {30}^{\circ }$
$=\frac{3}{4}\times \frac{3}{4}+1\times \frac{1}{2}\times \frac{1}{2}=\frac{9}{16}+\frac{1}{4}=\frac{13}{16}$