Solve the given equation. If there is no solution, enter NO SOLUTION: cos2x=5sinx-2?

I don't know how to start the problem.

1 Answer
Dec 3, 2017

Answer: x=pi/6+2pik,(5pi)/6+2pikx=π6+2πk,5π6+2πk, k in ZZ

Explanation:

Solve cos2x=5sinx-2

Note that cos(2x)=1-2sin^2(x)

Substituting in, we have:
1-2sin^2(x)=5sinx-2

Moving everything to one side:
2sin^2(x)+5sinx-3=0

We now have a quadratic which we can factor:
(2sinx-1)(sinx+3)=0

So, we have that sinx=1/2 or sinx=-3, clearly the latter is not possible since sinx in [-1,1]

Therefore x=pi/6+2pik,(5pi)/6+2pik, k in ZZ