Find the general solution of the equation sin2x+cosx=0

Asked by Pragya Singh | 1 year ago |  52

Solution :-

It is given that

sin 2x + cos x = 0

We can write it as

2 sin x cos x + cos x = 0

cos x (2 sin x + 1) = 0

cos x = 0 or 2 sin x + 1 = 0

Let cos x = 0

Or, $$sinx=-\dfrac{1}{2}$$

Hence we have,

$$x=(2n+1)\dfrac{\pi}{2}$$, where $$n \in Z$$

$$-sin=\dfrac{\pi}{6}$$

$$sin=(\pi-\dfrac{7\pi}{6})$$

$$sin=(\dfrac{7\pi}{6})$$

Which implies

$$x=nπ+(-1)^n\dfrac{7\pi}{6}$$, where $$n \in Z$$

Therefore, the general solution is$$(2n +1)\dfrac{\pi}{2}$$

or $$nπ+(-1)^n\dfrac{7\pi}{6}, n \in Z$$

Answered by Abhisek | 1 year ago

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