SSC CGL Model Paper 18

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Question : 69 of 100

Marks: +1, -0

If

\cosec ^2θ = 625 / 576

, then what is the value of

[(\sinθ - \cos θ) / (\sin θ + \cosθ)] ?

1
$31/17$
$17/31$
$14/25$

Solution:

\cosec θ = 625 / 576

⇒

\cosec^ 2θ = 25 /24

In right angle ΔACB, by Pythagoras theorem,

(A C )^2 =(AB)^2 - (B C )^ 2

= (25)^2 - (2 4 )^ 2

∴ AC = 7
∴

{ \sinθ - \cos θ} / {\sin θ + \cosθ }={14/25-7/25}/{24/25+7/25}=17/31

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