What is the general solution for sqrt(4sin(x)+7)=3 ?

The general solution for sqrt(4sin(x)+7)=3 is x= pi/6+2pin,x=(5pi)/6+2pin

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sqrt(4sin(x)+7)=3

4 sin (x) + 7 = 3

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

4 sin (x) + 7 = 3

Square both sides:

4 sin (x) + 7 = 9

4 sin (x) + 7 = 9

Solve

4 sin (x) + 7 = 9 : sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

Verify Solutions:

sin (x) = \frac{1}{2}

True

The solution is

sin (x) = \frac{1}{2}

General solutions for

sin (x) = \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

tan (θ) = \frac{2}{1}

cos (2 x) = sin^{2} (x)

sec^{2} (x) - 3 tan (x) = 5

sin (x) = 0, 4

What is the general solution for sqrt(4sin(x)+7)=3 ?
The general solution for sqrt(4sin(x)+7)=3 is x= pi/6+2pin,x=(5pi)/6+2pin