SSC CGL Tier II 21 Sep 2014 Paper

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Question : 44 of 100

Marks: +1, -0

Value of

\sec ^{2} \θ- {\sin ^{2} \θ-2 \sin ^{4} \θ}/{2 \cos ^{4} \θ-\cos ^{2} \θ}

is

1
2
–1
0

Solution:

(1)

\sec ^{2} \θ- {\sin ^{2} \θ-2 \sin ^{4} \θ}/{2 \cos ^{4} \θ-\cos ^{2} \θ}

=\sec ^{2} \θ- {\sin ^{2} \θ(1-2 \sin ^{2} \θ)}/{\cos ^{2} \θ(2 \cos ^{2} \θ-1 )}

=\sec ^{2} \θ- {\sin ^{2} \θ(1-2 (1-\cos ^{2} \θ) )}/{\cos ^{2} \θ(2 \cos ^{2} \θ-1 )}

=\sec ^{2} \θ-\tan ^{2} \θ{ (2 \cos ^{2} \θ-1 )}/{2 \cos ^{2} \θ-1}

=\sec ^{2} \θ-\tan ^{2} \θ=1

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