SSC CGL 26 Oct 2014 Shift 1 Paper

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Question : 127 of 200

Marks: +1, -0

sin^6

θ +

cos^6

θ is equal to

1
1 – 3 $sin^2 θ cos^2 θ$
1 – 3 sin θ cos θ
1 + 3 $sin^2 θ cos^2 θ$

Solution:

sin^6

θ +

cos^6

θ
=

(sin^2 θ )^3

+

(cos^2θ )^3

=

(sin^2 θ + cos^2θ )^3

– 3

sin^2

θ .

cos^2

θ (

sin^2

θ +

cos^2

θ )
[Since

a^3 + b^3

=

(a + b)^3

– 3ab (a + b)]
= 1 – 3

sin^2

θ .

cos^2

θ
because

sin^2θ + cos^2θ

= 1

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