SSC CPO SI and ASI Model Paper 8

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Question : 107 of 200

Marks: +1, -0

If sin

x + sin^2 x = 1

then

(cos^12 x + 3cos^10 x + 3cos^8 x + cos^6 x – 1)

is equal to

–2
2
0
1

Solution:

(3)

sin x + sin^2x = 1

sin x = 1 – sin^2 x = cos^2 x

∴ (cos^12 x + 3cos^10 x + 3cos^8 x +cos^6 x – 1)

= (cos^4 x + cos^2 x)3 – 1 [Since(A +B)^3 =A^3 +B^3+ 3AB^2 + 3A^2B ]

= (sin^2 x + cos^2 x)^3 – 1

= 1 – 1 = 0

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