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3 years ago

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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