Q (7) Find the general solution of the following equation 

\small \sin 2x + \cos x = 0

Answers (1)

sin2x + cosx = 0
We know that 
sin2x = 2sinxcosx
So, 
2sinxcosx + cosx = 0
cosx(2sinx + 1) = 0
So, we can say that either 

cosx = 0                                       or                           2sinx + 1 = 0
    x=(2n+1)\frac{\pi}{2}                                                          sinx =\sin\frac{7\pi}{6}
                                                                                               x=n\pi +(-1)^{n}\frac{7\pi}{6}
Therefore, the general solution is

 x=(2n+1)\frac{\pi}{2}    or   n\pi +(-1)^{n}\frac{7\pi}{6} \ where \ n\in Z 

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