# 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

#### 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}

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