Required to Prove the following trig identity:

Question

(cos2x)^2 + (sin2x)^2 = 1

Answer 1

Can you use the Pythagorean theorem?

If so, draw a right trangle, label the sides, and angles.

change cosine x to adjacent/hyp
change sin x to opposite/hyp

substitute in the hypothesis:
(adj/hyp)^2 + (Opp/hyp)^2=1

(adj^2 + opp^2)/Hyp^2=1
hyp^2/hyp^2=1
1=1