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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

1 + sin^{4} (x)

from both sides

cos^{4} (x) - 1 - sin^{4} (x) = 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 cos^{2} (θ) - 11 cos (θ) - 1 = - 7 cos (θ)

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

sin (x) = cos (1 9^{\circ})

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

tan (A) = \frac{8}{15}

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