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= pi/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{π}{2} + 2 πn

Solution steps

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

Subtract

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{π}{2} + 2 πn

Combine all the solutions

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

sin^{2} (x) - 1 = 0, 0 \leq x < 2 π

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

sin^{4} (x) - cos^{4} (x) = 0

tan (θ) cos (θ) + cos (θ) = 0

sin (x) = cos (x), 0 \leq x \leq 2 π

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= pi/2+2pin