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

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

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

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

x = \frac{3 π}{4} + πn

Solution steps

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

Factor

sin^{3} (x) + cos^{3} (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) + 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{3 π}{4} + πn

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

No Solution

Combine all the solutions

x = \frac{3 π}{4} + πn

- sin (3 x) \cdot 3 = 0

2 sin (4 x) - 2 = 0

6 tan (x) sin (x) = 7 sin (x)

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

3 tan^{4} (x) - 10 tan^{2} (x) + 3 = 0

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