Question

express sin theta in terms of cot theta

Answer 1

$cot \theta= \frac{cos \theta}{sin \theta} \\ \\ squaring\ both\ sides\\ \\cot^2 \theta= \frac{cos^2 \theta}{sin^2 \theta}= \frac{1-sin^2 \theta}{sin^2 \theta}= \frac{1}{sin^2 \theta}-\frac{sin^2 \theta}{sin^2 \theta}\\ \\ \Rightarrow cot^2 \theta=\frac{1}{sin^2 \theta}-1\\ \\ \Rightarrow cot^2 \theta+1=\frac{1}{sin^2 \theta}\\ \\ \Rightarrow sin^2 \theta= \frac{1}{cot^2 \theta+1} \\ \\ \Rightarrow sin \theta= \frac{1}{\sqrt{cot^2 \theta+1}}$

$sin \theta\ will\ be\ positive\ since\ \theta\ is\ acute.$

Answer 2

Answer:

sin theta =√ 1/cos²theta + 1