Question of The Day05-10-2020

# If 3 cos 2a = n cos 8a, then what is the value of cot 5a cot 3a?

Correct Answer : b ) $$\frac{n+3} { n-3}$$

Explanation :

3 cos 2a = n cos 8a

$${n \over 3}={cos \ 2a \over cos \ 8a}$$

Using componendo dividendo

$${n+3 \over n-3}={cos \ 2a+cos \ 8a \over cos \ 2a-cos \ 8a}$$

We know,

$$cosA+cosB=2cos({A+B \over 2})cos({A-B \over 2})$$

$$cosA-cosB=2sin({A+B \over 2})sin({B-A \over 2})$$

Thus,

$${n+3 \over n-3}={2 \ cos \ 5a \ × \ cos \ 3a \over 2 \ sin \ 5a \ × \ sin \ 3a}$$

$$cot \ 5a \ cot \ 3a={n+3 \over n-3}$$

Hence, (b) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA, UP SI etc.

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