Prove

CosA to the power 4 - sinA to the power 4

Is =2CosA to the power 2

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Solution

Cos⁴A-sin⁴A
=(cos²A)²-(sin²A)²
=(cos²A+sin²A)x(cos²A-sin²A).....equation 1
since
Cos²A+sin²A=1
And cos²A-sin²A=cos2A=2cos²A-1
Putting these values in equation 1 we get
Cos⁴A-sin⁴A=2cos²A-1

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