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If $cos x + cos^{2}x$ = 1, the numerical value of $(sin^{12}x + 3 sin^{10}x + 3 sin^{8}x + sin^{6}x - 1)$ is :

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If $cos x + cos^{2}x$ = 1, the numerical value of $(sin^{12}x + 3 sin^{10}x + 3 sin^{8}x + sin^{6}x - 1)$ is :
1). -1
2). 2
3). 0
4). 1

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2 answers

3 vote
Answered by on | Votes 3 |
option 3 is the right answer

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0 vote
Answered by on | Votes 0 |

cos x + cos2 x = 1
=> cos x = 1 – cos2 x = sin2 x ...(i)
$\therefore$ sin12x + 3 sin10x + 3 sin8x +sin6x – 1
= (sin4 x + sin2 x)3 – 1
= (cos2 x + sin2x)3 – 1 [By (i)]
= 1 – 1 = 0 .




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