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,x= pi/2+2pin,x=(3pi)/2+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, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 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 + 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

2 sinh (x) - 2 cosh (x) - 2 = 0

sec^{2} (x) + cot^{2} (x) = csc^{2} (x)

\frac{sin ( 7 9 ^{\circ} )}{12} = \frac{sin ( B )}{7}

\frac{( sin ^{2} ( x ) )}{( 1 - cos ( x ) )} = 1.23

- 1 = tan (2 (0)^{3} + C)

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,x= pi/2+2pin,x=(3pi)/2+2pin