What is the value of \cot 45^{\circ}+\frac{1}{3} cosec 60^{\circ} ?

BA LLB Banaras Hindu University 2019 Solved Paper

Question : 126 of 170

Marks: +1, -0

What is the value of

\cot 45^{∘}+\;{1}/{3} cosec 60^{∘}

Solution:

\cot 45^{∘}+\;{1}/{3} cosec 60^{∘}

=1+\;{1}/{3}(\;{2}/{√{3}})

[ ∵ \cot 45^{∘}=1, cosec 60^{∘}=\;{2}/{√{3}}]

=\;{3 √{3}+2}/{3 √{3}}

....(i)

=\;{3 √{3}+2}/{3 √{3}} × \;{3 √{3}}/{3 √{3}}=\;{27+6 √{3}}/{27}

[multiply and divide Eq. (i) with

3 √{3}

]

=\;{3(9+2 √{3})}/{27}=\;{9+2 √{3}}/{9}

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