Question

Show that cos2x + 1 = 2cos2 x. Use the "^" key on the keyboard to indicate an exponent. For example, sin2 x would be typed as sin^2x.

Answer 1

cos2x+1=2cos²x

cos2x equals to cos²x-sin²x
1 equals to sin²x+cos²x
Then substitute:

cos²x-sin²x+sin²x+cos²x=2cos²x
cos²x+cos²x=2cos²x
2cos²x=2cos²x
Verified.