What is the general solution for 4cos^2(x)+4sqrt(3)sin(x)=7 ?

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

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4cos^2(x)+4sqrt(3)sin(x)=7

4 cos^{2} (x) + 43 sin (x) = 7

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Solution steps

4 cos^{2} (x) + 43 sin (x) = 7

Subtract

7

from both sides

4 cos^{2} (x) + 43 sin (x) - 7 = 0

Rewrite using trig identities

- 3 - 4 sin^{2} (x) + 4 sin (x) 3 = 0

Solve by substitution

sin (x) = \frac{3}{2}

sin (x) = \frac{3}{2} : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

cos (2 θ) - sin (θ) cos (θ) = 0

\frac{cos ( x )}{2} - \frac{1}{2} = 0

tan (x) = \frac{4}{7}

sin (x) = - \frac{8}{9}

cos^{2} (θ) + 2 cos (θ) = 3

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