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Functions question

2012 · Shift 2 · Q40

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PYQ Library
JEE Advanced
Mathematics
Functions
2012 · Shift 2 · Q40

Functions question

2012 · Shift 2 · Q40

JEE AdvancedMathematicsFunctionsMultiple correct+4 / −1

Let

f:( - 1,1) \to R

be such that

f(\cos 4\theta ) = {2 \over {2 - {{\sec }^2}\theta }}

for

\theta \in \left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 4},{\pi \over 2}} \right)

. Then the value(s) of

f\left( {{1 \over 3}} \right)

is(are)

A
$1 - \sqrt {{3 \over 2}}$
B
$1 + \sqrt {{3 \over 2}}$
C
$1 - \sqrt {{2 \over 3}}$
D
$1 + \sqrt {{2 \over 3}}$

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