Question

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

• A. $3$
• B. $2$
• C. $0$
• D. $1$

Answer 1

Answer: (D)

$1$

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

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

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