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SSC CGL 2025 PYQ — Question 23

SSC CGL Tier II - 18 January 2025 - Shift I • Quantitative Aptitude • Q23

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If secθ−tanθsecθ+tanθ=19,θ\frac{sec\theta-tan\theta}{sec\theta+tan\theta}=\frac 1 9, \theta lies in the first quadrant, then the value of sinθ−tan2θsinθ+tan2θ\frac{sin\theta-tan^2\theta}{sin\theta+tan^2\theta}  is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. −1129-\frac{11}{29}.

(secθ - tanθ) / (secθ + tanθ) = 1/9

⇒ (1/cosθ - sinθ/cosθ)/(1/cosθ + sinθ/cosθ) = 1/9

⇒ (1 - sinθ)/(1 + sinθ) = 1/9

⇒ 9 - 9sinθ = 1 + sinθ

⇒ 10sinθ = 8

⇒ sinθ = 8/10 = 4/5

⇒ cos2θ = 1 - sin2θ = 1 - (4/5)2 = 1 - 16/25 = 9/25

⇒ cosθ = 3/5

⇒ tanθ = sinθ/cosθ = (4/5)/(3/5) = 4/3

Now, (sinθ - tan2θ)/(sinθ + tan2θ) = [4/5 - (4/3)2]/[4/5 + (4/3)2]

= (4/5 - 16/9)/(4/5 + 16/9)

= (-44/45)/(116/45)

= -11/29

Therefore, the value of the given expression is -11/29.