Question

Will someone please help show me the process for solving the following equation?

solve the equation in the interval [0, 2pi]
2sintcost+sint-2cost-1=0

Answer 1

First, find the GCF
(sin x(2 cos x +1) -1(2 cos x +1) = 0

Then factor
(sin x -1)(2 cos x + 1) = 0

Then,
sin x - 1 = 0
Use arcsin to solve for x
x = arcsin (1)
Repeat that for cos

Based on that, (sin x-1)(2cos x + 1) = 0, is true when:
x = pi/2+-2pin, 2pi/3+-2pin, 4pi/3+-2pin