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

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

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

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

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

Solution steps

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

Subtract

cos^{2} (x) - 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

tan (x) = a, tan (x + 18 0^{\circ})

cos (x) (tan (x) csc (x))^{2} - 1 = 2 cos (x)

sin (a) = \frac{4}{6}

cos (a) = 0.94

2 cos (2 x) - 1 = 0

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