Question

The value of $\tan {80}^{\circ }\tan {10}^{\circ }+{\sin }^2{70}^{\circ }+{\sin }^2{20}^{\circ }$ is

• A. $0$
• B. $1$
• C. $2$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is C $2$

$\tan 80\times \tan 10+{\sin }^{2}70+{\sin }^{2}20$
Now, $\tan {80}^{\circ }=\cot (90-80{)}^{\circ }=\cot {10}^{\circ }....(1)$
Also, $\sin {70}^{\circ }=\cos (90-70{)}^{\circ }=\cos {20}^{\circ }.....(2)$
From $\left(1\right)$ and $\left(2\right)$
$=\cot {10}^{\circ }\times \tan {10}^{\circ }+{\cos }^2{20}^{\circ }+{\sin }^{2}20$
$=1+1=2$.