11 points LaPCalc 1055008 ommaseparated list Solve the equat

-11 points LaPCalc 105.5.008 omma-separated list Solve the equation. (Find all solutions of the equation in the interval [ 8 sin(2x) sin(x) 8 cos(x) Need Help?LRedWatch Watch It

Solution

8 sin (2x) sin x = 8 cos x

sin 2 x = 2 sin x cos x

8 * 2 sin x cos x sin x = 8 cos x

16 sin^2 x cos x - 8 cos x = 0

8 cos x ( 2 sin^2 x -1 ) = 0

8 cos x = 0

2 sin ^2 x -1 = 0

sinx = +- 1 / sqrt 2

soltuions are

x = pi/4 , 3pi/4 , 5pi/4 , 3pi/2 , pi/2 , 7pi/4