#### Question

If tanθ = 1 them, find the values of

\[\frac{\sin\theta + \cos\theta}{\sec\theta + cosec\theta}\]

#### Solution

tan*θ* = 1

We know that, tan45º = 1

∴ *θ *= 45º

Now,

\[\sin45^\circ = \frac{1}{\sqrt{2}}\]

\[\cos45^\circ = \frac{1}{\sqrt{2}}\]

\[\sec45^\circ = \sqrt{2}\]

\[cosec45^\circ = \sqrt{2}\]

\[\therefore \frac{\sin\theta + \cos\theta}{\sec\theta + cosec\theta} = \frac{\sin45^\circ + \cos45^\circ}{\sec45^\circ + cosec45^\circ} = \frac{\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}}{\sqrt{2} + \sqrt{2}} = \frac{\frac{2}{\sqrt{2}}}{2\sqrt{2}} = \frac{1}{2}\]

Is there an error in this question or solution?

Solution If Tanθ = 1 Them, Find the Values of Sin θ + Cos θ Sec θ + C O S E C θ Concept: Application of Trigonometry.