What is the general solution for cos(x)+cos^2(x)-sin^2(x)=0 ?

The general solution for cos(x)+cos^2(x)-sin^2(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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cos(x)+cos^2(x)-sin^2(x)=0

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

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

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

x, 2 sin (x) + csc (x) = 0

4 cos^{2} (x) + 4 = 6

sin (2 x + \frac{π}{6}) = - \frac{1}{2}

sin (θ) = - \frac{11}{6}

tan (θ) = \frac{3}{1}

What is the general solution for cos(x)+cos^2(x)-sin^2(x)=0 ?
The general solution for cos(x)+cos^2(x)-sin^2(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin