Question

$\frac{{\cos }^4\theta -{\sin }^4\theta }{{\cos }^2\theta -{\sin }^2\theta }=$

• A. $1$
• B. $2$
• C. $\cos$ $\theta$ $+\sin$ $\theta$
• D. $\cos$ $\theta$ $-\sin$ $\theta$

Answer 1

The correct option is A $1$

The value of $\frac{{\cos }^4\theta -{\sin }^4\theta }{{\cos }^2\theta -{\sin }^2\theta }$

$=\frac{({\cos }^2\theta +{\sin }^2\theta \left)\right({\cos }^2\theta -{\sin }^2\theta )}{({\cos }^2\theta -{\sin }^2\theta )}$

$={\cos }^2\theta +{\sin }^2\theta$

$=1$ ...... (Since, ${\sin }^2\theta +{\cos }^2\theta =1$)