242/MR00. problem / Math - Solved Math Problems

MR-242 / 1175. problem

Simplify the following expression:

$\cos^{2} x - \cos^{4} x + \sin^{4} x$

\cos^{2} x - \cos^{4} x + \sin^{4} x

c o s^{2} x - c o s^{4} x + s i n^{4} x

= c o s^{2} x (1 - c o s^{2} x) + \sin^{4} x

= c o s^{2} x \cdot s i n^{2} x + \sin^{4} x

= s i n^{2} x (c o s^{2} x + s i n^{2} x)

= s i n^{2} x

$c o s^{2} x - c o s^{4} x + s i n^{4} x = s i n^{2} x$

MathReference - Problems