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

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

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sin^4(x)-cos^4(x)=0

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

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

Solution steps

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

Factor

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

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

Rewrite using trig identities

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

Solving each part separately

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

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

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

Combine all the solutions

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

tan (θ) cos (θ) + cos (θ) = 0

sin (x) = cos (x), 0 \leq x \leq 2 π

3 cos (θ) = 0

2 sin^{2} (θ) + sin (θ) - 9 = 2 sin (θ) - 8

cos (θ) = \frac{5}{3}

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