Trigonometry is a branch of mathematics which deals with the study of angles, sides, and triangles. It has a lot of practical applications in fields such as engineering, physics, and architecture. In Class 11, students learn about the basic concepts of trigonometry, including the six trigonometric ratios, inverse trigonometric functions, and their properties. Here are some important formulas that students should know in order to excel in their Class 11 trigonometry exams.

**Basic Trigonometric Ratios**

The basic trigonometric ratios are the sine, cosine, and tangent of an angle. These ratios are used to find the length of the sides of a right triangle. The formulas for these ratios are:

- Sin θ = Opposite/Hypotenuse
- Cos θ = Adjacent/Hypotenuse
- Tan θ = Opposite/Adjacent

**Reciprocal Trigonometric Ratios**

The reciprocal trigonometric ratios are the cosecant, secant, and cotangent of an angle. These ratios are used to find the length of the sides of a right triangle. The formulas for these ratios are:

- Cosec θ = 1/Sin θ
- Sec θ = 1/Cos θ
- Cot θ = 1/Tan θ

**Pythagorean Trigonometric Identity**

The Pythagorean trigonometric identity is used to find the length of the hypotenuse of a right triangle. The formula for this identity is:

- Sin² θ + Cos² θ = 1

**Sum and Difference Trigonometric Formulas**

The sum and difference formulas are used to find the trigonometric functions of the sum or difference of two angles. The formulas for these identities are:

- Sin (A + B) = Sin A Cos B + Cos A Sin B
- Sin (A - B) = Sin A Cos B - Cos A Sin B
- Cos (A + B) = Cos A Cos B - Sin A Sin B
- Cos (A - B) = Cos A Cos B + Sin A Sin B
- Tan (A + B) = (Tan A + Tan B)/(1 - Tan A Tan B)
- Tan (A - B) = (Tan A - Tan B)/(1 + Tan A Tan B)

**Double Angle Trigonometric Formulas**

The double angle formulas are used to find the trigonometric functions of the double of an angle. The formulas for these identities are:

- Sin 2θ = 2 Sin θ Cos θ
- Cos 2θ = Cos² θ - Sin² θ
- Tan 2θ = (2 Tan θ)/(1 - Tan² θ)

**Half Angle Trigonometric Formulas**

The half angle formulas are used to find the trigonometric functions of half of an angle. The formulas for these identities are:

- Sin (θ/2) = ±√((1 - Cos θ)/2)
- Cos (θ/2) = ±√((1 + Cos θ)/2)
- Tan (θ/2) = ±√((1 - Cos θ)/(1 + Cos θ))

In conclusion, these are some of the important formulas that students should know in order to excel in their Class 11 trigonometry exams. It is important to practice these