Question

The value of $\frac{{\cos }^2{33}^o-{\cos }^2{57}^o}{{\sin }^2{\left(\frac{21}{2}\right)}^o-{\sin }^2{\left(\frac{69}{2}\right)}^o}$, is

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

Answer 1

Answer: (A)

$-\sqrt{2}$

$\frac{{\cos }^{2}33-{\cos }^{2}57}{\sin \frac{21}{2}-{\sin }^2\frac{69}{2}}$

$\frac{(1-{\sin }^{2}33)-(1-{\sin }^{2}57)}{{\sin }^2\frac{21}{2}-{\sin }^2\frac{69}{2}}$

$\frac{{\sin }^{2}57-{\sin }^{2}33}{{\sin }^2\frac{21}{2}-{\sin }^2\frac{69}{2}}$

$\frac{\sin (57+33)\sin (57-33)}{\sin (\frac{21}{2}+\frac{69}{2})\sin (\frac{21}{2}-\frac{69}{2})}$

$\frac{\sin 90\sin 24}{\sin 45(-\sin 24)}$

$\frac{1}{\frac{-1}{\sqrt{2}}}$

$-\sqrt{2}$