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Multiple Choice Questions
1. $$cot^{3}A$$ is equal to
(A): $$3cotA - cot^3A/(1 - 3cot^2A)$$
(B): $$3cotA + cot^3A/(1 - 3cot^2A)$$
(C): $$3cotA - cot^3A/(1 + 3cot^2A)$$
(D): $$3cotA + cot^3A/(1 + 3cot^2A)$$
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By: anil on 05 May 2019 02.13 am
We know that $$cot 2A = frac{cot^2 A - 1}{2 cot A}$$ and $$cot (A + B) = frac{(cot A . cot B - 1)}{cot A + cot B}$$ Expression : $$cot 3A = cot (2A + A)$$ = $$frac{(cot A . cot 2A - 1)}{cot A + cot 2A}$$ Now, $$(cot A . cot 2A - 1) = cot A (frac{cot^2 A - 1}{2 cot A}) - 1$$ = $$frac{cot^3 A - cot A - 2 cot A}{2 cot A} = frac{cot ^3A - 3 cot A}{2 cot A}$$ --------------(i) And, $$(cot A + cot 2A) = cot A + (frac{cot^2 A - 1}{2 cot A})$$ = $$frac{2 cot^2 A + cot^2 A - 1}{2 cot A} = frac{3 cot^2 A - 1}{2 cot A}$$ ----------------(ii) Dividing eqn(i) by (ii), we get : = $$frac{cot^3 A - 3 cot A}{3 cot^2 A - 1}$$ = $$frac{3 cot A - cot^3 A}{1 - cot^2 A}$$
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SSC CHSL 23 Jan 2017 Afternoon Shift
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