Question

if csc(theta)=10 what are the values of cos(theta) and cot(theta)

Answer 1

\[cosec \theta =10 \rightarrow \sin \theta =\frac{1}{cosec \theta}\]
\[\sin \theta =\frac{1}{10}\]
\[\cos^2 \theta = 1-\sin^2 \theta \]
\[= 1- (\frac{1}{10})^2\]
\[=1- \frac{1}{100} = \frac{100-1}{100}=\frac{99}{100}\]
\[\cos \theta = \sqrt{0.99}=0.9949\]