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

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

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

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

x = \frac{π}{2} + πn

Solution steps

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

Subtract

cos^{2} (x) + 1

from both sides

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

Rewrite using trig identities

- 1 - cos (2 x) = 0

Move

1

to the right side

- cos (2 x) = 1

Divide both sides by

- 1

cos (2 x) = - 1

General solutions for

cos (2 x) = - 1

2 x = π + 2 πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

tanh (x) = 1

tan (θ) = \frac{1}{3}

sin (θ) = \frac{20}{29}

2 cos (\frac{1}{2} x) - 3 = 0

4 cos (θ) = 2

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