Question

Find the general solution of sin 3x + cos 2x= -2​

Answer 1

Answer:Use the double angle expression for the cosine to write cos(2x) in terms of sin(x). Write 3x=2x+x and use an expression for sin(A+B) to write sin(2x+x)in terms of the sine and cosine of x and 2x. Use the double angle expression for sin(2x) and cos(2x) to write sin(3x) in terms of sin(x) and cos(x).Using these expressions you should now be able to write the equation sin(3x)=cos(2x) entirely in terms of sin(x). Substitute z=sin(x) and simplify to obtain a cubic equation in z.

You should be able to spot a solution to this cubic equation and then use long division to obtain a quadratic which you can solve and then have all three solutions to the cubic equation in z. Decide which of these solutions give you a value of x with 0<x<90o.

Step-by-step explanation: