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Question Number 95324 by I want to learn more last updated on 24/May/20

If \sin A + {(\sin A)}^{2} = 1

Then the value of

{(\cos A)}^{12} + 3 {(\cos A)}^{10} + 3 {(\cos A)}^{8} + {(\cos A)}^{6} - 1 is ?

(a) 0

(b) 1

(c) - 1

(d) 2

Commented by bobhans last updated on 24/May/20

\sin^{2} A + \sin A - 1 = 0 \Rightarrow \sin A = \frac{- 1 \pm \sqrt{5}}{2}

1 - \cos^{2} A + \sin A - 1 = 0

\sin A = \cos^{2} A

\Rightarrow \cos^{6} A {\cos^{6} A + 3 \cos^{4} A + 3 \cos^{2} A + 1} - 1

Commented by bobhans last updated on 24/May/20

\cos^{4} A = \sin^{2} A \Rightarrow \cos^{6} A = \sin^{3} A .

now it easy to solve

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