Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. 5 cos4(x)

Answer 1

5COS(4x) = 5COS(2x + 2x) = 5(COS(2x)COS(2x) - SIN(2x)SIN(2x))

= 5( COS(2x)² - SIN(2x)² ) Squaring both COS and SIN

= 5( COS(2x)² - (1 - COS(2x)² )) Substituting for SIN(2x)

=5( 2COS(2x)² - 1) Combining terms

1st Power Form =5( 2(1-SIN(x)²)² -1) Substituting for COS(2x)