What is the general solution for cos^3(x)-sin^3(x)=0 ?

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

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cos^3(x)-sin^3(x)=0

cos^{3} (x) - sin^{3} (x) = 0

x = \frac{π}{4} + πn

Solution steps

cos^{3} (x) - sin^{3} (x) = 0

Factor

cos^{3} (x) - sin^{3} (x) : (cos (x) - sin (x)) (cos^{2} (x) + sin (x) cos (x) + sin^{2} (x))

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

Rewrite using trig identities

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

Solving each part separately

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

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

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

No Solution

Combine all the solutions

x = \frac{π}{4} + πn

2 sec (θ) + 3 = 0

3 sec^{2} (x) - 5 tan (x) = 3

sin (2 x) cos (6 x) - cos (2 x) sin (6 x) = - 0.55

\frac{1}{cos ( x )} = - 1

3 tan^{3} (θ) - tan (θ) = 3 tan^{2} (θ) - 1

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