5cos2x+2sin2x*tg2x+7=0

Question

5cos2x+2sin2x*tg2x+7=0

Answer 1

5cos2x+2sin2x*tg2x+7=0
5cos^2x+2sin^2x+7cos2x=0
sin^2x=1-cos^2x
5cos^2x+2-2cos^2x+7cos2x=0  cos2x=t
3t^2+7t+2=0 
(-7+-5)/6  t=-2  - |t|<=1<br>t=-1/3  cos2x=-1/3
x=1/2(П+-arccos(1/3))+Пk