Question

${\cos }^4\theta +{\sin }^4\theta =$

• A. $\frac{1}{4}(\cos 4\theta -3)$
• B. $\frac{1}{8}(\cos 4\theta -3)$
• C. $\frac{1}{4}(\cos 4\theta +3)$
• D. $\frac{1}{8}(\cos 4\theta +3)$

Answer 1

The correct option is C $\frac{1}{4}(\cos 4\theta +3)$

${\cos }^4\theta +{\sin }^4\theta =({\sin }^2\theta +{\cos }^2\theta {)}^2-2{\cos }^2\theta {\sin }^2\theta$
$=1-\frac{{\sin }^{2}2\theta }{2}$
$=1-\frac{(1-\cos 4\theta )}{4}$
$=\frac{1}{4}(\cos 4\theta +3)$
Hence, option 'C' is correct.