Question

Which of the following are identities? Check all that apply.
a. sin2x = 1 + cos2x
b. sin2x + cos2x = 1
c. tan2x = 1 - sec2x
d. cot2x + 1 = csc2x

Answer 1

To be an identity, the equality needs to hold regardless of the value of \(x\). The Pythagorean theorem will be of help here:\[\sin^2 \theta + \cos^2 \theta = 1\]Try dividing both sides by \(\sin^2\theta\) or \(\cos^2\theta\) to get some different forms.