What is the general solution for cos^4(x)-sin^4(x)=1 ?

The general solution for cos^4(x)-sin^4(x)=1 is x=2pin,x=pi+2pin

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cos^4(x)-sin^4(x)=1

cos^{4} (x) - sin^{4} (x) = 1

x = 2 πn, x = π + 2 πn

Solution steps

cos^{4} (x) - sin^{4} (x) = 1

Subtract

1

from both sides

cos^{4} (x) - sin^{4} (x) - 1 = 0

Apply exponent rule:

a^{b} = a^{2} a^{b - 2}

- 1 - sin^{4} (x) + cos^{2} (x) cos^{2} (x) = 0

Rewrite using trig identities

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

Divide both sides by

- 2

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

4 sec^{2} (x) tan (x) = 8 tan (x)

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

tan (2 x) = tan (x)

tan^{2} (x) = - 1

3 cot^{2} (θ) - 1 = 0

What is the general solution for cos^4(x)-sin^4(x)=1 ?
The general solution for cos^4(x)-sin^4(x)=1 is x=2pin,x=pi+2pin