Question

The value of cos ${}^{2}10^{\circ }-cos10^{\circ }cos50^{\circ }+co{s}^{2}50^{\circ }$

• A. $\frac{3}{2}(1+cos20^{\circ })$
• B. $\frac{3}{4}$
• C. $\frac{3}{4}+cos20^{\circ }$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$\frac{1}{2}(2co{s}^{2}10^{\circ }-2cos10^{\circ }cos50^{\circ }|+2co{s}^{2}50^{\circ })$
$\Rightarrow \frac{1}{2}(1+cos20^{\circ }-(cos60^{\circ }+cos40^{\circ })+1+cos100^{\circ })$
$\Rightarrow \frac{1}{2}(\frac{3}{2}+cos20^{\circ }+2sin70^{\circ }sin(-30^{\circ }))$
$\Rightarrow \frac{1}{2}(\frac{3}{2}+cos20^{\circ }-sin70^{\circ })$
$\Rightarrow \frac{3}{4}$