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SSC CHSL 2023 PYQ — Question 72

SSC CHSL - 08 Aug 2023 - Shift 1 • Quantitative Aptitude • Q72

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If secθsec\theta = 24232\frac{4}{23},  find the value of tan2θtan^2\theta.

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 33845293\frac{384}{529}.

Given, secθsec\theta = 24232\frac{4}{23} 

⇒ secθ=5023sec\theta = {50 \over 23}

⇒ sec2θ=2500529sec^2\theta = {2500 \over 529}

Now, sec2θ−tan2θ=1sec^2\theta - tan^2\theta = 1

⇒ sec2θ−1=tan2θsec^2\theta - 1 = tan^2\theta

⇒ tan2θ=2500529−1tan^2\theta = {2500 \over 529} - 1

⇒ tan2θ=1971529tan^2\theta = {1971 \over 529}

⇒ tan2θ=3384529tan^2\theta = 3{384 \over 529}