Question

if sec theta = √3 find cot theta and sin theta of trigonometry ratio.​

Answer 1

Answer:

$cot\theta=\dfrac{1}{\sqrt{2}}$

$sin\theta=\dfrac{\sqrt{2}}{\sqrt{3}}$

Step-by-step explanation:

Given,

$sec\theta=\sqrt{3}$

To Find :

$cot\theta,sin\theta$

Solution :-

We know that :-

$sec\theta=\dfrac{hypotenuse}{adjacent\:side}$

$\implies \dfrac{\sqrt{3}}{1}=\dfrac{hypotenuse}{adjacent\:side}$

Hypotenuse = √3 , adjacent side = 1

Let ,

opposite side be 'x'

We know that :-

$(hypotenuse)^2=(adjacent\:side)^2+(opposite\:side)^2$

$(\sqrt{3})^2=1^2+x^2$

$3 = 1 + x^2$

$x^2 = 3 - 1$

$x^2=2$

$opposite\:side=x=\sqrt{3}$

$cot\theta=\dfrac{adjacent\:side}{hypotenuse}$

$cot\theta=\dfrac{1}{\sqrt{2}}$

$sin\theta=\dfrac{opposite\:side}{hypotenuse}$

$sin\theta=\dfrac{\sqrt{2}}{\sqrt{3}}$