Question

if theta=45° then 1-cos²theta/sin²theta​

Answer 1

Answer:

1

Step-by-step explanation:

Given,

$\theta = 45\degree$

To Find :-

$\dfrac{1 -cos^2\thetha}{sin^2\theta}$

Solution :-

$\dfrac{1 -cos^2\thetha}{sin^2\theta}$

$\dfrac{1 -cos^245\degree}{sin^245\degree}$

$cos45\degree = \dfrac{1}{\sqrt{2}}$

$sin45\degree = \dfrac{1}{\sqrt{2}}$

$= \dfrac{1 -\bigg (\dfrac{1}{\sqrt{2}}\bigg)^2}{\bigg(\dfrac{1}{\sqrt{2}}\bigg)^2}$

$= \dfrac{1 - \dfrac{1}{2}}{\dfrac{1}{2}}$

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

= 1