Question

solve for all real numbers, 2cos^2x + 7sinx = 5

Answer 1

Answer:

2cos x + 7 sin x=5

2(1-sin x)+7sin x=5

2-2sin x +7sin x + 3=0

2sin x - 6sin x - sin x + 3=0

2sin x (sin x-3)-1(sin x-3)=0

(sin x-3)(2sin x - 1)=0

sin x=3 OR 2 sin x-1=0

sin x=3 is impossible

sin x=1/2 = -1 = 1/2 =1