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# Ex.8.3 Q5 Introduction to Trigonometry Solution - NCERT Maths Class 10

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## Question

If $$\,{\rm{sec}}4A = {\rm{cosec}}\left( {A-20^\circ } \right),$$where $$4A$$ is an acute angle, find the value of $$A$$.

Video Solution
Introduction To Trigonometry
Ex 8.3 | Question 5

## Text Solution

#### Steps:

Given that: $$\text{sec} \;4\;A= \text{cosec} (A -20^{\circ})$$….(i)

Since, $$\sec A = {\rm{cosec}}\,\left( {{{90}^0} - A} \right)$$

By using property in equation (i) we get:

\begin{align} {\rm{cosec}}\left( {{\rm{9}}{{\rm{0}}^\circ} - 4A} \right) &= {\rm{cosec}}\left( {A - {{20}^\circ}} \right)\\ {90^\circ} - 4A &= A - {20^\circ}\\ 5A &= {110^\circ}\\ A &= \frac{{{{110}^\circ}}}{5}\\ &= {22^\circ}\\ A &= {22^\circ} \end{align}

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