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

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

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4cos(x)=sin^2(x)-2-3cos^2(x)

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

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

Subtract

sin^{2} (x) - 2 - 3 cos^{2} (x)

from both sides

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

Rewrite using trig identities

1 + 4 cos (x) + 4 cos^{2} (x) = 0

Solve by substitution

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x, ln (y) = arctan (x) + C

sin (x) + 2 sin (x) = 5

cos (θ) = - \frac{3}{10}

2 cos^{3} (x) = 0

50 sin (x) + 15 cos (x) = 40, 0 < x < π

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