AP ICET 2019 Shift 1 Paper

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Question : 120 of 200

Marks: +1, -0

If sec θ + tan θ =

2/3

, then in θ =

- $5/{13}$
- $5/{12}$
${12}/{13}$
$5/6$

Solution:

\secθ + \tanθ =2/3

...(1)

\secθ-\tanθ =3/2

...(2)
(As

\sec^2θ-\tan^2θ = 1

).
On adding (1) & (2) we get

2\secθ =13/6

or

\sec θ={13}/{12} ⇒ \cos θ={12}/{13}

(1)-(2)

⇒ \tan θ={-5}/{12}

∴ \sin θ=\tan θ × \cos θ={-5}/{12} × {12}/{13}={-5}/{13}

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