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

The general solution for sin^4(x)=1-cos^4(x) is x=2pin,x=pi+2pin,x= pi/2+2pin,x=(3pi)/2+2pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

1 - cos^{4} (x)

from both sides

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

Apply exponent rule:

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

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = - 1, cos (x) = 0

cos (x) = 1 : x = 2 πn

cos (x) = - 1 : x = π + 2 πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

8 cos (\frac{1}{2} x) + 4 = 0

5 sin (2 t) = 0

3 tan (3 x) + 3 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

2 tan (θ) + 4 = tan (θ) + 5

x, sin (x) = \frac{4}{5}

What is the general solution for sin^4(x)=1-cos^4(x) ?
The general solution for sin^4(x)=1-cos^4(x) is x=2pin,x=pi+2pin,x= pi/2+2pin,x=(3pi)/2+2pin