SSC CGL 9 Aug 2015 Shift 1 Paper

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Question : 112 of 200

Marks: +1, -0

The maximum value of

sin^4 θ + cos^4 θ

is

$1/3$
1
2
3

Solution:

Expression
=

sin^4 θ + cos^4 θ

=

(sin^2 θ)^2 + (cos^2 θ)^2

=

(sin^2 θ + cos^2 θ)^2

– 2

sin^2 θ

.

cos^2 θ

.
= 1 – 2

sin^2 θ. cos^2 θ

= 1 -

{4sin^2 θ . cos^2 θ}/2

= 1 -

{sin^2 2θ}/2

= 1 -

{1-cos4θ}/4

= 1 -

1/4 + {cos4θ}/4

= 1 -

1/4+1/4

= 1

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