The value of \tan ^{-1} [\frac{1}{2} \cos ^{-1} ( {\sqrt{5}}/{3}) ] is

CBSE Class 12 Math 2020 Outside Delhi Set 3 Solved Paper

Note : Except for the following questions, all the remaining questions have been asked in the previous sets.

SECTION - A

Question : 1 of 11

Marks: +1, -0

The value of

\tan ^{-1} [\;{1}/{2} \cos ^{-1} (\;{{√{5}}}/{3}) ]

Solution:

y=\tan [\;{1}/{2} \cos ^{-1} (\;{{√{5}}}/{3}) ]

Let,

x=\cos ^{-1} (\;{{√{5}}}/{3})

⇒ \cos x=\;{{√{5}}}/{3}

∴ y=\tan \;{1}/{2} x

y=\tan \;{x}/{2}

y=√{\;{1-\cos x}/{1+\cos x}}

=√{\;{1-{{√{5}}}/{3}}/{1+\;{{√{5}}}/{3}}}

=√{\;{3-{√{5}}}/{3+{√{5}}}}

rationalizing the factor, we get,

{\y}=\;{3-{√{5}}}/{2}

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