Question

The value of ${\cos }^4\theta -{\sin }^4\theta +2{\sin }^2\theta$ is equal to

• A. $0$
• B. ${\sin }^2\theta$
• C. ${\cos }^2\theta$
• D. $1$

Answer 1

Answer: (D)

$1$

${\cos }^4\theta -{\sin }^4\theta +2{\sin }^2\theta$
$=({\cos }^2\theta {)}^2-{\sin }^4\theta +2{\sin }^2\theta$
$=(1-{\sin }^2\theta {)}^2-{\sin }^4\theta +2{\sin }^2\theta$
$=1-2{\sin }^2\theta +{\sin }^4\theta -{\sin }^4\theta +2{\sin }^2\theta$
$=1$
Hence answer is D