Question

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

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Step-by-step explanation:

• cos8a+sin8a=1−sin2(2a)+18sin4(2a).

1==14=(sin2a+cos2)4=sin8a+4sin6acos2a+6sin4acos4a+4sin2acos6a+cos8a.

Isolate the LHS of the desired identity in the RHS of the above identity, and manipulate what it is equal to, remembering sin(2a)=2sinacosa

• sin8a+cos8a=====1−4sin6acos2a−6sin4acos4a−4sin2acos6a=1–4sin2acos2a(sin4a+cos4a)−32(2sin2acos2a)2=1−sin2(2a)[(sin2a+cos2a)2−2sin2acos2a]−38sin4(2a)=1−sin2(2a)+12sin4(2a)−38sin4(2a)=1−sin2(2a)+18sin4(2a)

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