Question

What is ${\sin }^{2}66\frac{1^o}{2}-{\sin }^{2}23\frac{1^o}{2}$ equal to?

• A. $\sin {47}^o$
• B. $\cos {47}^o$
• C. $2\sin {47}^o$
• D. $2\cos {47}^o$

Answer 1

The correct option is B $\cos {47}^o$

$\frac{1-\cos {123}^{\circ }}{2}-\frac{1-\cos {47}^{\circ }}{2}$

we know that,

$\cos (\pi -{123}^{\circ })=-\cos {47}^{\circ }$

hence,

Ans, $\cos {47}^{\circ }$