Question

Cotteeta=1 1+cotteeta/sinteeta

Answer 1

Given:

$\cot \theta$ = 1

We have to find, the value of $\dfrac{1+\cot \theta}{\sin \theta}$ is:

Solution:

∴ $\cot \theta$ = $\dfrac{1}{1} =\dfrac{b}{p}$

Here, base, b = 1 and perpendicular, p = 1

By Pythagoras Theorem,

Hypotaneous, h = $\sqrt{p^{2}+b^{2} }$

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

= $\sqrt{2}$

$\sin \theta$ = $\dfrac{p}{h} =\dfrac{1}{\sqrt{2}}$

∴ $\dfrac{1+\cot \theta}{\sin \theta}$

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

= 2$\sqrt{2}$

Thus, the value of $\dfrac{1+\cot \theta}{\sin \theta}$ is equal to "2$\sqrt{2}$".