Question

If tan $\theta$ =1, then the value of $\frac{sin\theta +cos\theta }{sec\theta -cosec\theta }$,

Answer 1

Given: $\tan \theta =1$

$\tan \theta =\tan {45}^{\circ }$

$\theta ={45}^{\circ }$

$\frac{\sin \theta +\cos \theta }{\sec \theta +cosec\theta }$

= $\frac{\sin 45+\cos 45}{\sec 45+cosec45}$

= $\frac{\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{\sqrt{2}+\sqrt{2}}$

= $\frac{\frac{2}{\sqrt{2}}}{2\sqrt{2}}$

= $\frac{2}{4}$

= $\frac{1}{2}$