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Ivenika [448]
3 years ago
7

Sin^4a+cos^4a -sin^6a+cos^6a= sin^2a cos^2a

Mathematics
1 answer:
dsp733 years ago
7 0

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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