Question #24c10

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Answer 1 · 2017-02-09T02:53:17

Explained below

In the numerator on the left side add and subtract 1 as,

$1+tan^2 theta +cos^2 theta -1$

or, $1+tan^2 theta -( 1-cos^2 theta)$

or, $sec^2 theta - sin^2 theta$

or, $1/(cos^2 theta) - sin^2 theta$ . Now factorise it,

$(1/cos theta - sin theta)(1/cos theta + sin theta)$

The factor $(1/ cos theta + sin theta)$ would get cancelled out with the denominator, leaving with the factor $1/cos theta - sin theta$ = RHS