AP ICET 2016 Paper

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Question : 129 of 200

Marks: +1, -0

If

0<θ<\;\;{π}/{2}

and

\tanθ+\secθ=3

,then

sinθ=

$1/2$
$4/5$
$1/5$
$√3/2$

Solution:

Given :

\Secθ+\tanθ=3,0 < θ < π/2

⇒\Secθ-\tanθ=1/3\;\;\;\;[\sec^2θ-\tan^2θ=1]

Adding we get, 2 sec θ

=3+1/3=10/3

⇒\cosθ=3/5

θ lies in the first quadrant.

∴\sinθ√{1-(3/5)^2}=4/5

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