Question

How to solve this trigonometric equation?

Answer 1

Do you have in your textbook the method to convert an expression of the form a cos x + b sin x into c sin(x + phi)? That method works well here to solve the equation.

Answer 2

Write u=sin(x), v=cos(x).

You have 2 equations:

u+sqrt(3)v=sqrt(2)

u^2 +v^2 =1

So how do you relate them? You can:

- Use the first equation to write u in term of v

- Then substitute into the second equation to get a quadratic equation

- Then solve for v, and then u