Question

Sin^8A-cot^8A =1-4sin^2A.cos^2A+2sin^4A.cos^4A

Answer 1

Answer:

Step-by-step explanation:

(sin^2A + cos^2 A) = 1

Raising to square both sides yields:

(sin^2 A + cos^2 A)^2 = 1^2

sin^4 A + 2sin^2A cos^2 A +cos^4 A = 1

You need to isolate the sum sin^4 A + cos^4  A to the left side such that:

sin^4 A + cos^4 A = 1 - 2sin^2A cos^2 A

You need to raise to square both sides such that:

(sin^4 A + cos^4 A) = (1 - 2sin^2A cos^2 A)^2

sin^8 A + 2sin^4 Acos^4 A + cos^8 A = 1 - 4sin^2A cos^2 A + 4sin^4 A cos^4 A

Moving to the right 2sin^4 Acos^4 A  yields:

sin^8 A +cos^8 A = 1 - 4sin^2A cos^2 A + 4sin^4 A cos^4 A - 2sin^4 Acos^4  A

sin^8 A + cos^8 A = 1 - 4sin^2A cos^2 A + 2sin^4 A cos^4 A

Hence, checking if the given identity holds yields that, using the fundamental formula of trigonometry, the identity sin^8 A + cos^8 A = 1 - 4sin^2A cos^2 A + 2sin^4 A cos^4 A  is valid.

Answer 2

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