Find the exact solutions of the equation in the interval 0 2

Find the exact solutions of the equation in the interval [0, 2pi). (Enter your answers as a comma-separated list.) cos 2x + sin x = 0 x =________ Use a double-angle formula to rewrite the expression. 16 sin^2 x - 8__________

Solution

1) cos2x +sinx =0

(1-2sin²x)+sinx=0

2sin²x -sinx -1=0

2sin²x -2sinx+sinx -1=0

2sinx(sinx -1)+1(sinx-1)=0

(2sinx+1)(sinx -1)=0

sinx =-1/2,sinx=1

x=7pi/6 ,11pi/6 , pi/2

5)16sin²x -8

=8(2sin²x -1)

=-8(1-2sin²x)

=-8cos(2x)