Ex.8.3 Q3 Introduction to Trigonometry Solution - NCERT Maths Class 10

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Question

Q3. If \({\rm{tan}}2A = {\rm{cot}}\left( {A-18^\circ } \right)\) , where \(2A\) is an acute angle, find the value of \(A.\)

Text Solution

 

Reasoning:

\(\tan ({90^0} - \theta ) = \cot \theta \)

Steps:

Given that:

\({\rm{tan}}2{\rm{A}} = {\rm{cot}}\left( {{\rm{A}}-18^\circ } \right)\)…....(i)

But \(\tan 2{\rm{A}} = \cot \,({90^0} - 2{\rm{A}}) \)

By substituting this in equation (i) we get:

\[\begin{align} \cot \,\left( {{{90}^0} - 2A} \right) &= \cot \,\left( {A - {{18}^0}} \right)\\ {90^0} - 2A &= A - {18^0}\\ 3A &= {108^0}\\ A &= \frac{{{{108}^0}}}{3} = {36^0}\\ A &= {36^0} \end{align}\]