Question

if tan 2a= cot (a-18), where 2a is an acute angel, find the value of a

Answer 1

Tan 2 A = Cot (A-18)

As Tan(90-Θ) = CotΘ, Then

Tan 2 A = Tan (90-(A-18))

Cancelling Tan on both sides,

2 A = 90 - A + 18

3 A = 108

   A = 36°
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Answer 2

The answer is given below :

Now,

$tan \: 2a = cot \: (a - 18) \\ \\ or \: \: cot \: (90 - 2a) = cot(a - 18) \\ \\ or \: \: 90 - 2a = a - 18 \\ \\ or \: \: 3a = 108 \\ \\ so\: \: a = 36$

Thus, a = 36°

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