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If \( \Large sec \theta +tan \theta =2 \), what is the value of \( \Large sec \theta \) ?

A) \( \Large \frac{3}{2} \)
B) \( \Large \sqrt{2} \)
C) \( \Large \frac{5}{2} \)
D) \( \Large \frac{5}{4} \)

Correct Answer:




D) \( \Large \frac{5}{4} \)

Description for Correct answer:
By trigonometric identity,

\( \Large sec^{2} \theta -tan^{2} \theta =1 \)

=> \( \Large (sec \theta +tan \theta )(sec \theta -tan \theta )=1 \)

=> \( \Large sec \theta -tan \theta =\frac{1}{2} \) ....(i)

and given, \( \Large sec \theta +tan \theta =2 \) .....(ii)

On adding Eqs. (i) and (ii), we get

\( \Large 2sec \theta=\frac{1}{2}+2 \)

\( \Large sec \theta =\frac{5}{4} \)

Part of solved Trigonometry questions and answers : >> Elementary Mathematics >> Trigonometry

Comments

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