What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos⁴x- sin⁴x is the same as cos2x. Is cos⁸x-sin⁸x = cos2x also true? Thank you.

Jon
Student
High School Precalc

If you know the formulas for angle sums like cos(a+b), then use them with a = 2x and b = x. As for (cosx)⁴ - (sin x)⁴, it is simply a happy accident why it equals (cos x)² - (sin x)². You should understand why it is true and why the same accident does not happen with the 8th powers.