# Question #bb3f7

##### 1 Answer

Jan 17, 2016

#### Explanation:

The first step is to rewrite

#cos(2x)=cos^2(x)-sin^2(x)# #cos^2(x)=1-sin^2(x)# #cos(2x)=1-sin^2(x)-sin^2(x)=1-2sin^2(x)#

Thus, the function can be rewritten as

#1-2sin^2(x)+2sin(x)-3=-2#

Move all the terms to the same side.

#0=2sin^2(x)-2sin(x)#

Divide both sides by

#sin^2(x)-sin(x)=0#

Factor a

#sin(x)(sin(x)-1)=0#

Here, we have a product of two terms that equals

#sinx=0color(white)(ssssss)"or"color(white)(ssssss)sin(x)-1=0=>sin(x)=1#

#x=picolor(white)(ssssssskl)"or"color(white)(ssssssssssssssssssssssss)x=pi/2#

The times when