NIMCET 2012 Question Paper with solutions

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Question : 11 of 120

Marks: +1, -0

If

sin^2 x

= 1 - sin x , then

cos^4

x +

cos^2

x is equal to

0
1
$2/3$
- 1

Solution:

Given

sin^2 x

= 1 - sin x
⇒

1-cos^2x

= 1 - sin x
⇒ sin x =

cos^2

x ... (i)
Now ,

cos64 x+cos^2 x

=

(cos^2 x)^2

+

cos^2x

=

(sinx)^2

+ sin x
=

sin^2 x

+ sin x
= (1 - sin x) + sin x [from Eq. (i)]
= 1

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