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SSC CGL 2022 PYQ — Question 51

SSC CGL - 01 Dec 2022 - Shift 4 • Quantitative Aptitude • Q51

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16cos⁡3π6−12cos⁡π6=________.16{\cos ^3}\frac{{\rm{\pi }}}{6} - 12\cos \frac{{\rm{\pi }}}{6} = \_\_\_\_\_\_\_\_.

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 0

Concept used:

Trigonometry value based method

Calculations:

We know that cosπ6=30ocos \frac{\pi}{6} = 30^o

And, value of cos 30° = 32\frac{\sqrt3}{2}

Now, according to the question,

⇒ 16 cos3 30° - 12 cos 30°

⇒ 16 × (√3/2)3 - 12 × (√3/2)

⇒ 16 × 3√3/8 - 6√3

⇒ 6√3 - 6√3 = 0