Sin^6x + cos^6x = 1/4

for integer (including negative numbers.)

Step-by-step explanation:

Pythagorean Identity: . Equivalently, .

Rewrite the original equation and apply this substitution to eliminate :

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Let (.) The original equation is equivalent to the following equation about :

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Expand the cubic binomial in the equation:

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Simplify to obtain:

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Rearrange and simplify:

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Solve for :

Either or .

If , then for all .

On the other hand, if , then for all .

Combine both situations to obtain:

for all .

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step-by-step explanation: