What is the general solution for cos(x)=sin^2(x)-1 ?

The general solution for cos(x)=sin^2(x)-1 is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin

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cos(x)=sin^2(x)-1

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

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

Solution steps

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

Subtract

sin^{2} (x) - 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 0, cos (x) = - 1

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

sin (x) cot (x) - sin (x) = 0

tan (θ) = \frac{1}{7}

2 tan (x) + cos (x) = 0

cos (2 x) + sec (2 x) = 11

cos^{2} (t) = \frac{3}{4}

What is the general solution for cos(x)=sin^2(x)-1 ?
The general solution for cos(x)=sin^2(x)-1 is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin