Question

Find the general solution of sin 2x=4cosx

Answer 1

Answer:

sin2x=4cosx

Step-by-step explanation:

sin2x=4cosx

sin(2x)-4cos(x)=0

then,

2sin(x) cos(x)- 4 cos(x)=0.....sin2x= 2sinxcosx

cos(x)( 2sin(x)- 4)=0

hence

cosx= 0

x=cos^1(0)

x= π/2 +2πk........ where k is an integral

Answer 2

The general solution of given equation is $x=n\pi-\frac{\pi}{2}$ where, n is any integer.

Step-by-step explanation:

The given equation is

$\sin 2x=4\cos x$

We need to find the general solution of given equation.

Taking all variable terms on the left side.

$\sin 2x-4\cos x=0$

$2\sin x\cos x-4\cos x=0$              $[\because \sin 2x=2\sin x\cos x]$

Taking out common factors.

$2\cos x(\sin x-2)=0$

Divide both sides by 2.

$\cos x(\sin x-2)=0$

Using zero product property we get

$(\sin x-2)=0\rightarrow \sin x=2$

It is not possible because the value of sin x lies in the interval [-1,1].

$\cos x=0$

$x=n\pi-\frac{\pi}{2}$

where, n is any integer.

Therefore, the general solution of given equation is $x=n\pi-\frac{\pi}{2}$ where, n is any integer.

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