Question

The general solution of the equation sin 2x + 2sin x + 2cos x +1 =0 is:

• A. \(3n\pi-\dfrac{\pi}{4}\)
• B. \(2n\pi+\dfrac{\pi}{4}\)
• C. \(2n\pi+(-1)^n\sin^{-1}\!\left(\dfrac{1}{\sqrt{3}}\right)\)
• D. nπ-(π)/(4)

Hint:

Convert sums of sine and cosine into single trigonometric form.

Answer 1

The Correct Option is D

Rearranging and factoring leads to: sin x+cos x=-\frac1√(2) Thus, x=nπ-(π)/(4)