Question

HELP A FELLA OUT Please

Answer 1

I'll write "x" instead theta.

sin x + 1 = cos(2x)

formula: cos(2x) = 1 - 2sin²x

sin x + 1 = 1 - 2sin²x

2sin²x + sin x = 0

sin x (2sin x + 1) = 0

sin x = 0 or sin x = -1/2

x1 = πk and x2 = -π/6 + 2πk and

x3 = 5π/6 + 2πk

for domain 0≤x<2π :

x1 = 0 (for k=0 in x1)

x2 = π (for k=1 in x1

x3 = 11π/6 (for k=1 in x2)

x4 = 5π/6 (for k=0 in x3).

k is an integral.