If \(\tan\theta = 1\), then find the value of \(\dfrac{\sin\theta + \cos\theta}{\sec\theta + \operatorname{cosec}\theta}\) by completing the following activity.Activity :\(\tan\theta = 1\) ......... (given)but \(\tan ____ = 1\)\(\therefore \theta = _…

Q.3 (A)(1) If \(\tan\theta = 1\), then find the value of \(\dfrac{\sin\theta + \cos\theta}{\sec\theta + \operatorname{cosec}\theta}\) by completing the following activity.

Activity :

\(\tan\theta = 1\) ......... (given)

but \(\tan ____ = 1\)

\(\therefore \theta = ____\)

\(\therefore \dfrac{\sin\theta + \cos\theta}{\sec\theta + \operatorname{cosec}\theta} = \dfrac{\sin 45^\circ + \cos 45^\circ}{\sec 45^\circ + \operatorname{cosec} 45^\circ}\)

\(= \dfrac{\dfrac{1}{____} + \dfrac{1}{\sqrt2}}{\sqrt2 + ____}\)

\(= \dfrac{\dfrac{2}{\sqrt2}}{____}\)

\(\dfrac{\sin\theta + \cos\theta}{\sec\theta + \operatorname{cosec}\theta} = \dfrac{1}{____}\)