Question

1) If Ian 2A = cot(A - 18⁰) where 2A in an
acute angle Find the value of a ,​

Answer 1

To Find:-

• The value of A

Given:-

• Tan2A = Cot(A - 18°)
• 2A is an acute angle (less than 90°).

Concept:-

First we have to evaluate Tan2A in the terms of CotA.Then equate it and find the value of A.We know that

• Tanθ= Cot(90 - θ)

Equate it and then find the value of A in the above mentioned question.The value of A should be below 90° because it is specified that A is an acute angle.

Solution:-

$\Large\mathtt{Tan2A \: = Cot(A \: - \: 18)}$

We know that,

• Tanθ= Cot(90 - θ)
• So,

$\implies\large\mathtt{Cot(90 \: - \: 2a) = Cot(A \: - \: 18)}$

$\implies\large\mathtt{(90 \: - \: 2A) = (A \: - \: 18)}$

$\implies\large\mathtt{ - 2A \: - \: A \: = \: -18 \: - \: 90}$

$\implies\large\mathtt{ -3A \: = \: - 108}$

$\implies\large\mathtt{ A \: = \: \frac{ - 108}{ - 3} }$

$\implies\large\mathtt{A \: =\:36}$