What is the general solution for sin^4(θ)-cos^4(θ)=0 ?

The general solution for sin^4(θ)-cos^4(θ)=0 is θ= pi/4+pin,θ=(3pi)/4+pin

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sin^4(θ)-cos^4(θ)=0

sin^{4} (θ) - cos^{4} (θ) = 0

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

Solution steps

sin^{4} (θ) - cos^{4} (θ) = 0

Factor

sin^{4} (θ) - cos^{4} (θ) : (sin^{2} (θ) + cos^{2} (θ)) (sin (θ) + cos (θ)) (sin (θ) - cos (θ))

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

Rewrite using trig identities

(- cos (θ) + sin (θ)) (cos (θ) + sin (θ)) = 0

Solving each part separately

- cos (θ) + sin (θ) = 0 or cos (θ) + sin (θ) = 0

- cos (θ) + sin (θ) = 0 : θ = \frac{π}{4} + πn

cos (θ) + sin (θ) = 0 : θ = \frac{3 π}{4} + πn

Combine all the solutions

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

9 + 9 sin (θ) = 6 cos^{2} (θ)

cot (x) = \frac{1}{2}

sec (t) = 3

tan (θ) = - \frac{12}{5}

x, sin (2 x) = sin (x)

What is the general solution for sin^4(θ)-cos^4(θ)=0 ?
The general solution for sin^4(θ)-cos^4(θ)=0 is θ= pi/4+pin,θ=(3pi)/4+pin