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

The general solution for 4cos(x)+sin^2(x)=3cos^2(x)+2 is x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Subtract

3 cos^{2} (x) + 2

from both sides

4 cos (x) + sin^{2} (x) - 3 cos^{2} (x) - 2 = 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{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

5 tan (B) + 13 = 0

tan^{2} (x) = 3 tan (x)

2 cos^{2} (x) - 2 = 0

sin (θ - \frac{π}{4}) - 1 = 0

tan^{2} (x) + csc^{2} (x) - 3 = 0

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