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 \(A\).

Text Solution

 

Reasoning:

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

Steps:

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

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

By using property in equation (i) we get:

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