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SSC CGL 2021 PYQ — Question 70

SSC CGL - 16 Aug 2021 - Shift 3 • Quantitative Aptitude • Q70

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If sin⁡(2A+B2)=cos⁡(2A−B2)=32\sin(\frac{2A+B}{2}) = \cos(\frac{2A-B}{2}) = \frac{\sqrt3}{2} where 0<(2A+B2)<900 < (\frac{2A+B}{2}) < 90  and 0<(2A−B2)<900 < (\frac{2A-B}{2}) < 90 then, find the value of sin (3(A-B))

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Correct answer: B

Explanation

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

Calculations :

⇒ sin(2A + B)/2 = 3/2\sqrt3/2

⇒ (2A + B)/2 = sin-1(3/2\sqrt3/2)

⇒ (2A + B)/2 = 60°

⇒ (2A + B) = 120°       ----- (1)

Now, cos(2A - B)/2 = 3/2\sqrt3/2

⇒ (2A - B)/2 = cos-1(3/2\sqrt3/2)

⇒ (2A - B)/2 = 30°

⇒ (2A - B) = 60°       ----- (2)

Solving equations (1) and (2), we get

⇒ A = 45° and B = 30°

Putting the values of A and B, we get

⇒ sin (3(A - B))

⇒ sin (3(45 - 30))

⇒ sin (3(15))

⇒ sin 45°

⇒ 1/21/\sqrt2