If secθ = 54, then tan θ2 =

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Question

If sec

θ

=

\frac{5}{4}

, then tan

\frac{θ}{2}

=

Options:

A . 13

B . 34

C . 14

D . 19

Answer: Option A
:
A
Given that sec

θ

=

\frac{5}{4}

sec

θ

=

\frac{1 + t a n^{2} (\frac{θ}{2})}{1 - t a n^{2} (\frac{θ}{2})}

\Rightarrow

\frac{5}{4}

=

\frac{1 + t a n^{2} (\frac{θ}{2})}{1 - t a n^{2} (\frac{θ}{2})}

\Rightarrow

5 - 5 t a n^{2} (\frac{θ}{2}) = 4 + 4 t a n^{2} (\frac{θ}{2})

\Rightarrow

9 t a n^{2} (\frac{θ}{2})

= 1

\Rightarrow

t a n (\frac{θ}{2})

=

\frac{1}{3}

.

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