Question

sin⁸a+cos⁸a= 1/8(8 -8Sin²2a+Sin⁴2a)​

Answer 1

Answer:

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).

And there you have it. Easy every time.

Step-by-step explanation:

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