Answer to Question #146976 in Trigonometry for Hazel

Question

Sin(y)+sin(y)cot^2(y)=cosec(y)

Answer 1

Explanations & Calculations

• Start the proof with the Left hand side as there are more terms present

$\qquad\qquad \begin{aligned} \small \sin y +\sin y \cot^2 y &=\small\sin y (1+\cot^2 y)\\ &=\small \sin y\Big(1+\frac{\cos^2 y}{\sin^2 y}\Big)\\ &= \small \sin y \Big(\frac{\sin^2 y+\cos^2 y}{\sin^2 y}\Big)\\ &=\small \sin y\times \frac{1}{\sin^2 y}\\ &=\small\frac{1}{\sin y}\\ &= \small \cosec y\\ \end{aligned}$