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

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

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

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

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

Solution steps

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

Subtract

2 - 5 cos (x)

from both sides

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

Rewrite using trig identities

- 3 + 2 cos^{2} (x) + 5 cos (x) = 0

Solve by substitution

cos (x) = \frac{1}{2}, cos (x) = - 3

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 3 :

No Solution

Combine all the solutions

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

tan (\frac{x}{4}) = - 3

8 sin^{2} (x) - 2 sin (x) - 1 = 0, - \frac{π}{2} < x < \frac{π}{2}

cos (4 x) - cos (3 x) = 0

2 cos^{2} (A) + cos (A) - 1 = 0

tan^{3} (x) = tan (x), 0 \leq x \leq 2 π

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