Question

if p cot theta = whole root of q^2- p^2, then find the value of sin theta

Answer 1

Answer:This may help

Step-by-step explanation:

Answer 2

Answer:

$sin\theta=\frac{p}{q}$

Step-by-step explanation:

Given : ${\text{p cot} \theta= \sqrt{q^2-p^2}$

To Find : $Sin \theta$

Solution:

$cot \theta= \frac{\sqrt{q^2-p^2}}{p}$

Squaring both sides

$cot^2 \theta= \frac{q^2-p^2}{p^2}$

Identity : $cot^2 \theta = Cosec^2 \theta - 1$

So, $Cosec^2 \theta - 1= \frac{q^2-p^2}{p^2}$

$Cosec^2 \theta= \frac{q^2-p^2}{p^2}+1$

$Cosec^2 \theta= \frac{q^2-p^2+p^2}{p^2}$

$Cosec^2 \theta= \frac{q^2}{p^2}$

Property : $cosec \theta = \frac{1}{sin\theta}$

So, $\frac{1}{sin^2\theta}= \frac{q^2}{p^2}$

$sin^2\theta= \frac{p^2}{q^2}$

$sin\theta=\sqrt{ \frac{p^2}{q^2}}$

$sin\theta=\frac{p}{q}$

Hence $sin\theta=\frac{p}{q}$