Question

If tan2A= cot (A – 18°) , where 2A is an acute angle , find the value of A

Answer 1

Step-by-step explanation:

tan2A=cot(A-18°)

cot(90°-2A)=cot(A-18°)

90°-2A=A-18°

3A=108

A=108/3

A=36

Answer 2

Hey Pretty Stranger!

$\bold{ \red {Here \: you \: go}}$

Given : tan2A= cot(A-18°)

To Find : The value of A

We know that,

$\rightarrow \tt \tan \theta = \cot(90 - \theta) \: and \\ \rightarrow\tt\: \cot \theta = \tan(90 - \theta)$

$\longrightarrow \tt \: \cot(90 - 2A) = \cot( A- 18)$

$\longrightarrow \tt \: 90 - 2A = A - 18$

$\longrightarrow \tt \: 90 + 18 = 2A + A$

$\longrightarrow \tt \: 108= 3A$

$\longrightarrow \tt \: A = \cancel\dfrac{108}{3}$

$\longrightarrow \tt \: A = \cancel\dfrac{108}{3}$

$\longrightarrow \tt \: A = \large\boxed{ \red{ \sf \: 36^{o} }}$

Hence,Value of A = 36°