Trigonometric Identities

\(\tan \theta=\frac{\sin \theta}{\cos \theta}\)

   2. Pythagorean Identity :

\( \cos ^2 \theta+\sin ^2 \theta=1\) 

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

                     \(1+\cot ^2 \theta=\operatorname{cosec}^2 \theta \)

  3. Double angle identity : 

\(\sin 2 \theta=2 \sin \theta \cos \theta \)

\( \cos 2 \theta=\cos ^2 \theta-\sin ^2 \theta=2 \cos ^2 \theta-1=1-2 \sin ^2 \theta\) 

\(\tan 2 \theta=\frac{2 \tan \theta}{1-\tan ^2 \theta} \)

            4. Reciprocal identities 

csc θ = 1/sinθ

sec θ = 1/cosθ

           5. Co-function identities

 sin(90° – θ) = cosθ 

cos(90° – θ) = sinθ

6. Compound angle identities : \( \)

\(\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B \)

 \(\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B \)

\(\tan (A \pm B)=\frac{\tan A \pm \tan B}{1 \mp \tan A \tan B} \)