Sin2x*tgx-2cos^2(x)=5sinx-3

Question

Sin2x*tgx-2cos^2(x)=5sinx-3

Answer 1

sin2x = 2sinx*cosx  ;  cosx*tgx = sinx    ;   sin^2x*cos^2x=1

 

2sinx*cosx*tgx- 2cos^2(x) - 5sinx + 3=0

2sinx*sinx - 2cos^2(x) - 5 sinx + 3=0

2 sin^2(x) - 2cos^2(x) - 5sinx +3=0

2( sin^2(x) - cos^2(x)) - 5 sinx +3=0

2*1 - 5sinx + 3=0

5sinx = 5

sinx = 1

x = π/ 2 + 2πn