Sin^4a+cos^4a -sin^6a+cos^6a= sin^2a cos^2a
1 answer:
Answer:
steps below
Step-by-step explanation:
sin⁴a+cos⁴a = (sin²a+cos²a)² - 2 sin²a cos²a
= 1 - 2 sin²a cos²a
sin⁶a-cos⁶a = (sin²a+cos²a)³ - 3 sin²a cos²a (sin²a + cos²a)
= 1³ - 3 sin²a cos²a * 1
= 1 - 3 sin²a cos²a
sin⁴a+cos⁴a-sin⁶a+cos⁶a = (1 - 2 sin²a cos²a) -(1 - 3 sin²a cos²a)
= sin²a cos²a
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