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SSC CHSL 2023 PYQ — Question 59

SSC CHSL - 10 Aug 2023 - Shift 3 • Quantitative Aptitude • Q59

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If A=60° and B=30°, find the value of (tanA−tanB)(1+tanAtanB)(tan A-tanB)\over(1+tanAtanB)

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 13\frac{1}{\sqrt3}.

(tanA−tanB)(1+tanAtanB)(tan A-tanB)\over(1+tanAtanB)

=(tan60∘−tan30∘)(1+tan60∘tan30∘)={(tan 60^\circ-tan30^\circ)\over(1+tan60^\circ tan30^\circ)}

=(3−13)(1+3×13)={(\sqrt3-\frac{1}{\sqrt3})\over(1+\sqrt3\times \frac{1}{\sqrt3})}

=232={\frac{2}{\sqrt3}\over2}

=13=\frac{1}{\sqrt3}

Therefore, the value of the expression is 1/√3.