If,
sin A + sin² A + sin³ A = 1,
then find the value of
cos⁶A - 4cos⁴ A + 8cos²A ?
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Answer:
sin A(1+sinA+ sin^2A) = 1
sin A (cos^2A+ sinA)= 1
cos^2AsinaA + sin^2A = 1
cos^2AsinaA = 1- sinA^2
cos^2AsinaA = cos^2A
sinA = 1
cos^2A = 1+ sin^2A
= 1+ (1)^2
= 2
cos^6A - 4cos^4A + 8cos^2A
= (cos^2A)^3 - 4 ((cos^2A)^2) + 8 cos^2A
= (2)^3 - 4((2)^2) +8 × 2
= 8 -16+16
= 8
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