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SSC CGL 2023 PYQ — Question 68

SSC CGL - 18 July 2023 - Shift 1 • Quantitative Aptitude • Q68

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Using trigonometric formulas, find the value of (sin(x−y)sin(x+y))(\frac{sin(x-y)}{sin(x+y)}) (tanx+tanytanx−tany)(\frac{tan x + tan y}{tan x - tan y})

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 1.

let's assume x = 60°

y = 30°

  (sin(x−y)sin(x+y))(\frac{sin(x-y)}{sin(x+y)}) (tanx+tanytanx−tany)(\frac{tan x + tan y}{tan x - tan y}) =   (sin(60−30)sin(60+30))(\frac{sin(60-30)}{sin(60+30)}) (tan60+tan30tan60−tan30)(\frac{tan60 + tan 30}{tan 60- tan 30})

= 1/2 × (3+133−13)(\frac{\sqrt3 + \frac{1}{\sqrt3}}{ \sqrt3-\frac{1}{\sqrt3}})

=  1/2 × 4/2

= 1