Question

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

• A. $3$
• B. $2$
• C. $0$
• D. $1$

Answer 1

The correct option is D $1$

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

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

$=\frac{({\sin }^2\theta -{\cos }^2\theta )({\sin }^2\theta +{\cos }^2\theta )}{{\sin }^2\theta -{\cos }^2\theta }$ ....... $[\because a^2-b^2=(a-b\left)\right(a+b\left)\right]$

$={\sin }^2\theta +{\cos }^2\theta =1$

Hence, $\frac{{\sin }^4\theta -{\cos }^4\theta }{{\sin }^2\theta -{\cos }^2\theta }=1$