Question

If tanθ = 1 them, find the values of $\frac{\mathrm{sin\theta }+\mathrm{cos\theta }}{\mathrm{sec\theta }+\mathrm{cosec\theta }}$ .

Answer 1

tanθ = 1

We know that, tan45º = 1

∴ θ = 45º

Now,

$$\begin{gathered} \sin 45°=\frac{1}{\sqrt{2}} \\ \cos 45°=\frac{1}{\sqrt{2}} \\ \sec 45°=\sqrt{2} \\ \mathrm{cosec}45°=\sqrt{2} \end{gathered}$$
$\therefore \frac{\sin \theta +\cos \theta }{\sec \theta +\mathrm{cosec}\theta }=\frac{\sin 45°+\cos 45°}{\sec 45°+\mathrm{cosec}45°}=\frac{{\displaystyle \frac{1}{\sqrt{2}}}+{\displaystyle \frac{1}{\sqrt{2}}}}{\sqrt{2}+\sqrt{2}}=\frac{{\displaystyle \frac{2}{\sqrt{2}}}}{2\sqrt{2}}=\frac{1}{2}$