Question

p=sinθ and q=4cotθ
show that p^(2)q^(2)=16(1-p^(2))

Answer 1

$$p = \sin \theta , \qquad q = 4 \cot \theta$$

Show that $p^2 q^2 = 16(1 - p^2)$

**Solution:**

$$\begin{array}{l} p^2 q^2 = \sin^2 \theta * 4^2 * \cot^2 \theta = 16 \sin^2 \theta * \frac{\cos^2 \theta}{\sin^2 \theta} = 16 \cos^2 \theta = 16(1 - \sin^2 \theta) \\ \equiv 16(1 - p^2) \end{array}$$