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

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

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

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

x = \frac{π}{2} + πn

Solution steps

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

Subtract

1 + cos^{2} (x)

from both sides

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

cos^{2} (θ) = 0

cos (7 x) cos (2 x) + sin (7 x) sin (2 x) = \frac{1}{2}

sin (2 x) = \frac{1}{2}, 0 \leq x \leq 2 π

8 sin^{2} (θ) - 6 = 0

3 sin (x) - cos (x) = 0

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