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

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

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

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

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

Solution steps

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

Subtract

cos (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

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

Combine all the solutions

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

sin (2 θ) = \frac{a}{5}

cos (a) = - \frac{1}{4}

\frac{cos ^{2} ( x ) - 4}{cos ( x ) - 2} = 1

- 8 sec^{2} (x) - 26 tan (x) = 12

tan (θ) = 0.3

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