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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

1 - sin^{2} (x)

from both sides

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

Rewrite using trig identities

- sin^{2} (x) = 0

Divide both sides by

- 1

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) + 0.65 = 0

sin^{2} (x) = 0.12

6 cos (x) = - 32

cos (x) = \frac{7}{12}

5 tan (x) + 3 = 4 (1 + tan (x))

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