Ex.8.3 Q4 Introduction to Trigonometry Solution - NCERT Maths Class 10

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Question

If \(\tan A = \cot B\,,\) prove that \(A + B = {90^0}.\)

Text Solution

 

Reasoning:

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

Steps:

Given that:

\(\begin{align}\,\tan A = \cot B & & (i)\end{align}\)

We know that,

\(\tan A = \cot \left( {{{90}^0} - A} \right)\)

By substituting this in equation (i) we get:

\[\begin{align} \cot \,({90^0} - A) &= \cot B\\ {90^0} - A &= B\\ A + B &= {90^0} \end{align}\]