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SSC CGL 2018 PYQ — Question 42

SSC CGL Tier II Quant - 09/03/2018 • Quantitative Aptitude • Q42

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If sin(A − B) = 1/2 and cos(A + B) = 1/2, then what is the value of sin A cos A + sin2 A sin B cos B + cos3 A cos B tan A?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. None of these

Understanding

Application

sin(A − B) = 1/2 and 

cos(A + B) = 1/2

So,

A – B = 30°

And

A + B = 60°

So,

A = 45° and B = 15°

sin A cos A + sin2 A sin B cos B + cos3 A cos B tan A

= 1/2 sin2A + 1/2 sin2 A sin2B + cos3 A cos B tan A

Putting the values of A and B:

= 1/2 sin90° + 1/2 sin245° sin30° + cos345° cos15° tan45°

= 1/2 × 1 + 1/2 × 1/2 × 1/2 + 1/2√2 × (√3 + 1)/2√2 × 1

= 1/2 + 1/8 + (√3 + 1)/8

= (4 + 1 + √3 + 1)/8

= (6 + √3)/8