Certainly! Here’s a detailed overview of the key formulas from Chapter 3 of Class 11 Maths, which typically covers "Trigonometric Functions."

Trigonometric Ratios
- Sine (sin):
- \( \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} \)
- Cosine (cos):
- \( \cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)
- Tangent (tan):
- \( \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{\sin \theta}{\cos \theta} \)
- Cosecant (csc):
- \( \csc \theta = \frac{1}{\sin \theta} \)
- Secant (sec):
- \( \sec \theta = \frac{1}{\cos \theta} \)
- Cotangent (cot):
- \( \cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta} \)

Trigonometric Identities
- Pythagorean Identities:
- \( \sin^2 \theta + \cos^2 \theta = 1 \)
- \( 1 + \tan^2 \theta = \sec^2 \theta \)
- \( 1 + \cot^2 \theta = \csc^2 \theta \)

Angle Sum and Difference Formulas
- Sine:
- \( \sin(a + b) = \sin a \cos b + \cos a \sin b \)
- \( \sin(a - b) = \sin a \cos b - \cos a \sin b \)
- Cosine:
- \( \cos(a + b) = \cos a \cos b - \sin a \sin b \)
- \( \cos(a - b) = \cos a \cos b + \sin a \sin b \)
- Tangent:
- \( \tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b} \)
- \( \tan(a - b) = \frac{\tan a - \tan b}{1 + \tan a \tan b} \)

Double Angle and Half Angle Formulas
- Sine:
- \( \sin 2\theta = 2 \sin \theta \cos \theta \)
- Cosine:
- \( \cos 2\theta = \cos^2 \theta - \sin^2 \theta = 2\cos^2 \theta - 1 = 1 - 2\sin^2 \theta \)
- Tangent:
- \( \tan 2\theta = \frac{2\tan \theta}{1 - \tan^2 \theta} \)
These formulas are foundational in solving trigonometric problems and understanding advanced mathematical concepts. Make sure to practice applying them in various scenarios for better comprehension!