Question

3cota =4 the check whether -1-tan2a/1+tan2a=cot2a-sin2a

Answer 1

If 3cot A = 4/3 , check whether (1-tan2A)/(1+tan2A) = cos2A – sin2A or not

Report by 5834Subham 13.09.2017

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baditya

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99EkanshNimbalkar

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SOLUTION

Let ΔABC in which ∠B = 90º, A/q, cot A = AB/BC = 4/3 Let AB = 4k and BC = 3k, where k is a positive real number. By Pythagoras theorem in ΔABC we get. AC2 = AB2 + BC2 AC2 = (4k)2 + (3k)2 AC2 = 16k2 + 9k2 AC2 = 25k2 AC = 5k tan A = BC/AB = 3/4 sin A = BC/AC = 3/5 cos A = AB/AC = 4/5 L.H.S. = (1-tan2A)/(1+tan2A) = 1- (3/4)2/1+ (3/4)2 = (19/16)/(1+ 9/16) = (16-9)/(16+9) = 7/25 R.H.S. = cos2A – sin2A = (4/5)2 - (3/4)2

= (16/25) - (9/25) = 7/25 R.H.S. = L.H.S. Hence, (1-tan2A)/(1+tan2A) = cos2A – sin2A

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