Question

State true or false.
${\cos }^2\theta +{\sec }^2\theta =2+\sin \theta$ is a identity.

• A. True
• B. False

Answer 1

The correct option is B False

Verify this identity by putting $\theta =\frac{\pi }{4}$

$(\frac{1}{\sqrt{2}}{)}^2+(\sqrt{2}{)}^2=2\frac{1}{\sqrt{2}}$

$\frac{1}{2}+2=LHS=\frac{5}{2}$

$\sqrt{2}=RHS$

RHS is not equal to LHS

Hence it is false