1. Trigonometric identities:

\(Sin^2\theta+cos^2\theta = 1\)

\(1+ tan^2\theta = sec^2\theta\)

\(1+ cot^2\theta = cosec^2\theta\)
 
 
2. Trigonometric ratios:
 
\(sin \theta = \frac{opposite\ side}{hypotenus}\) \(cosec \theta = \frac{hypotenus}{opposite\ side}\)
\(cos \theta = \frac{Adjacent\ side}{hypotenus}\) \(sec \theta = \frac{opposite\ side}{Adjacent\ side}\)
\(tan \theta = \frac{opposite\ side}{Adjacent\ side}\) \(cot \theta = \frac {Adjacent\ side}{opposite\ side}\)
 
 
3. Reciprocal of trigonometry:
 
\(sin \theta = \frac{1}{cosec\theta}\) \(cosec\theta = \frac{1}{sin\theta}\)
\(cos\theta = \frac{1}{sec\theta}\) \(sec\theta = \frac{1}{cos\theta}\)
\(tan\theta = \frac{1}{cot\theta}\) \(cot\theta = \frac {1}{tan\theta}\)
\(tan\theta = \frac{sin\theta}{cos\theta}\) \(cot\theta = \frac{cos\theta}{sin\theta}\)
\(tan\theta = \frac{sec\theta}{cosec\theta}\) \(cot\theta = \frac{cosec\theta}{sec\theta}\)
 
 
4.  Velues of trigonometric ratios:
 
Trignometric ratio
30° 45° 60° 90°
\(sin \theta\)  \(0\) \(\frac{1}{2}\) \(\frac{1}{\sqrt{2}}\) \(\frac{\sqrt{3}}{2}\) \(1\)
\(cos \theta\) \(1\) \(\frac{\sqrt{3}}{2}\) \(\frac{1}{\sqrt{2}}\) \(\frac{1}{2}\) \(0\)
\(tan \theta\) \(0\) \(\frac{1}{\sqrt{3}}\) \(1\) \(\sqrt{3}\) not defined
\(cot \theta\) not defined \(2\) \(\sqrt{2}\) \(\frac{2}{\sqrt{3}}\) \(1\)
\(sec \theta\) \(1\) \(\frac{2}{\sqrt{3}}\) \(\sqrt{2}\) \(2\) not defined
\(cosec \theta\) not defined \(\sqrt{3}\) \(1\) \(\frac{1}{\sqrt{3}}\) \(0\)