### Home > A2C > Chapter 13 > Lesson 13.2.3 > Problem 13-131

13-131.

Show how to derive the double angle formulas for sin(2*x*) and cos(2*x*) by substituting *x* for both *α* and *β* in the formulas for sin(*α* + *β*) and cos(*α* + *β*), then simplifying. Homework Help ✎

sin(*x* + *x*) = sin(*x*)cos(*x*) + cos(*x*)sin(*x*) = 2sin(*x*)cos(*x*)

cos(*x* + *x*) = cos(*x*)cos(*x*) − sin(*x*)sin(*x*) = cos^{2}(*x*) − sin^{2}(*x*)