Question

Prove or disprove the identity. If you find the identity os true, state the first line of the proof. If yor find the identity is false, write the correct equation by replacing the right side.

Answer 1

We know of course

$\sin ^2 x + \cos^2 x = 1$

so we're left to show true or false,

$\tan^2 x + 1 = \csc^2 x$

$\dfrac{\sin^2 x}{\cos ^2 x} + 1 = \dfrac{\sin ^2 x + \cos^2 x}{\cos ^2x} = \dfrac{1}{\cos^2x} = \sec^2 x$

That's different than the identity because we got sec²x on the right.

Answer: D