Trigonometric formulas for CBSE Class 11:

### Basic Trigonometric Ratios:
1. **Sine (sin)**
\[
\sin \theta = \frac{\text{Opposite Side}}{\text{Hypotenuse}}
\]

2. **Cosine (cos)**
\[
\cos \theta = \frac{\text{Adjacent Side}}{\text{Hypotenuse}}
\]

3. **Tangent (tan)**
\[
\tan \theta = \frac{\text{Opposite Side}}{\text{Adjacent Side}} = \frac{\sin \theta}{\cos \theta}
\]

4. **Cosecant (csc or cosec)**
\[
\csc \theta = \frac{1}{\sin \theta} = \frac{\text{Hypotenuse}}{\text{Opposite Side}}
\]

5. **Secant (sec)**
\[
\sec \theta = \frac{1}{\cos \theta} = \frac{\text{Hypotenuse}}{\text{Adjacent Side}}
\]

6. **Cotangent (cot)**
\[
\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta} = \frac{\text{Adjacent Side}}{\text{Opposite Side}}
\]

### Reciprocal Identities:
1. \(\csc \theta = \frac{1}{\sin \theta}\)
2. \(\sec \theta = \frac{1}{\cos \theta}\)
3. \(\cot \theta = \frac{1}{\tan \theta}\)

### Pythagorean Identities:
1. \(\sin^2 \theta + \cos^2 \theta = 1\)
2. \(1 + \tan^2 \theta = \sec^2 \theta\)
3. \(1 + \cot^2 \theta = \csc^2 \theta\)

### Co-Function Identities:
1. \(\sin (90^\circ – \theta) = \cos \theta\)
2. \(\cos (90^\circ – \theta) = \sin \theta\)
3. \(\tan (90^\circ – \theta) = \cot \theta\)
4. \(\cot (90^\circ – \theta) = \tan \theta\)
5. \(\sec (90^\circ – \theta) = \csc \theta\)
6. \(\csc (90^\circ – \theta) = \sec \theta\)

### Even-Odd Identities:
1. \(\sin(-\theta) = -\sin \theta\)
2. \(\cos(-\theta) = \cos \theta\)
3. \(\tan(-\theta) = -\tan \theta\)
4. \(\cot(-\theta) = -\cot \theta\)
5. \(\sec(-\theta) = \sec \theta\)
6. \(\csc(-\theta) = -\csc \theta\)

### Sum and Difference Formulas:
1. \(\sin (A \pm B) = \sin A \cos B \pm \cos A \sin B\)
2. \(\cos (A \pm B) = \cos A \cos B \mp \sin A \sin B\)
3. \(\tan (A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}\)

### Double Angle Formulas:
1. \(\sin 2A = 2 \sin A \cos A\)
2. \(\cos 2A = \cos^2 A – \sin^2 A = 2 \cos^2 A – 1 = 1 – 2 \sin^2 A\)
3. \(\tan 2A = \frac{2 \tan A}{1 – \tan^2 A}\)

### Half Angle Formulas:
1. \(\sin \frac{A}{2} = \pm \sqrt{\frac{1 – \cos A}{2}}\)
2. \(\cos \frac{A}{2} = \pm \sqrt{\frac{1 + \cos A}{2}}\)
3. \(\tan \frac{A}{2} = \pm \sqrt{\frac{1 – \cos A}{1 + \cos A}} = \frac{\sin A}{1 + \cos A} = \frac{1 – \cos A}{\sin A}\)

### Product-to-Sum Formulas:
1. \(\sin A \sin B = \frac{1}{2} [\cos(A – B) – \cos(A + B)]\)
2. \(\cos A \cos B = \frac{1}{2} [\cos(A – B) + \cos(A + B)]\)
3. \(\sin A \cos B = \frac{1}{2} [\sin(A + B) + \sin(A – B)]\)

### Sum-to-Product Formulas:
1. \(\sin A + \sin B = 2 \sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A – B}{2} \right)\)
2. \(\sin A – \sin B = 2 \cos \left( \frac{A + B}{2} \right) \sin \left( \frac{A – B}{2} \right)\)
3. \(\cos A + \cos B = 2 \cos \left( \frac{A + B}{2} \right) \cos \left( \frac{A – B}{2} \right)\)
4. \(\cos A – \cos B = -2 \sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A – B}{2} \right)\)

These formulas are fundamental in solving various trigonometric problems and are essential for Class 11 students.