Question

Prove that: sin6ө + cos6ө=1- 3sin2өcos2ө

Answer 1

Step-by-step explanation:

sin⁶+ cos⁶

(sin²)³+(cos²)³

(sin²+cos²){(sin²)²-sin²•cos²+(cos²)²}

1(sin⁴-sin²•cos²+cos⁴)

(sin⁴-sin²•cos²+cos⁴)

(sin⁴+cos⁴-sin²•cos²)

{(sin²)²+(cos²)²-sin²•cos²}

{(sin²+cos²)²-2sin²•cos²-sin²•cos²}

(1²-3sin²•cos²)

1-3sin²cos²

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