What is the general solution for -5cos(x)=-2sin^2(x)+4 ?

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

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-5cos(x)=-2sin^2(x)+4

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

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

Solution steps

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

Subtract

- 2 sin^{2} (x) + 4

from both sides

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

Rewrite using trig identities

- 2 - 2 cos^{2} (x) - 5 cos (x) = 0

Solve by substitution

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

cos (x) = - 2 :

No Solution

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

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{2}{2}

sec^{2} (x) - 2 tan (x) = 4

cos (4 x) = cos (2 x)

sin (4 x) + sin (2 x) = 0

10 sin (x) tan (x) - 9 tan (x) = 0

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