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Implicit Differentiation

sin 2 A -cos ...

Question

(sin²A- cos²A) (1- 2sin²A. cos²A)=.

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Solution

(sin²a -cos²a)(1 - 2sin²a cos²a)
(sin²a - cos²a)(1)[(1)²-2sin²a cos²a]
= (sin²a - cos²a)(1)[(sin²a + cos²a)²- 2(sin²acos²a)]
= (sin²a - cos²a)(sin²a + cos²a)[(sin²a)²+ (cos²a)²]
(sin²a)²+ (cos²a)²= (sin²a + cos²a)²-2(sin²acos²a)
= (sin⁴a - cos⁴a)(sin⁴a + cos⁴a)
(sin⁴a)²- (cos⁴a)²
sin⁸a - cos⁸a

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