NIMCET 2011 Question Paper with solutions

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Question : 13 of 120

Marks: +1, -0

If

\sin x, \cos x

and

\tan x

are in

{GP}

, then

\cot ^{6} x-\cot ^{2} x

will be equal to

2
-1
1
0

Solution:

Since,

\cos ^{2} x=\sin x \tan x

⇒ \cos ^{3} x=\sin ^{2} x

....(i)

∴ \cot ^{6} x-\cot ^{2} x=\;{\cos ^{6} x}/{\sin ^{6} x}-\;{\cos ^{2} x}/{\sin ^{2} x}

=\;{\sin ^{4} x}/{\sin ^{6} x}-\;{\cos ^{2} x}/{\sin ^{2} x} \;\;

[from Eq. (i)]

=\;{1-\cos ^{2} x}/{\sin ^{2} x}

=\;{\sin ^{2} x}/{\sin ^{2} x}=1

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