What is the general solution for sin^6(x)-cos^6(x)=0 ?

The general solution for sin^6(x)-cos^6(x)=0 is x= pi/4+pin,x=(3pi)/4+pin

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sin^6(x)-cos^6(x)=0

sin^{6} (x) - cos^{6} (x) = 0

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

Solution steps

sin^{6} (x) - cos^{6} (x) = 0

Factor

sin^{6} (x) - cos^{6} (x) : (sin (x) + cos (x)) (sin^{2} (x) - sin (x) cos (x) + cos^{2} (x)) (sin (x) - cos (x)) (sin^{2} (x) + sin (x) cos (x) + cos^{2} (x))

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

Rewrite using trig identities

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

Solving each part separately

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

cos (x) sin (x) + 1 = 0 :

No Solution

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

No Solution

Combine all the solutions

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

- sin (2 x) sin (x) + cos (2 x) cos (x) = 0

sin (2 x) + cos (2 x) - 1 = 0

4 tan (x) sin^{2} (x) + 3 = 4 sin^{2} (x) + 3 tan (x)

tan (a) = 0.384

cos (b) = \frac{38}{70}

What is the general solution for sin^6(x)-cos^6(x)=0 ?
The general solution for sin^6(x)-cos^6(x)=0 is x= pi/4+pin,x=(3pi)/4+pin