Trigonometric Formula Class 11

List of some of the basic trigonometric formulas include the following formulas:

Pythagorean Identitis

• sin² θ + cos² θ = 1
• 1 + tan² θ = sec² θ
• cosec² θ = 1 + cot² θ

Co-Function Identitites

• sin (-θ) = -sin θ
• cos (-θ) = cos θ
• tan (-θ) = -tan θ
• cot (-θ) = -cot θ
• sec (-θ) = sec θ
• cosec (-θ) = -cosec θ

Complementary Angles Identities

• sin (90° – θ) = cos θ
• cos (90° – θ) = sin θ
• tan (90° – θ) = cot θ
• cot (90° – θ) = tan θ
• sec (90° – θ) = cosec θ
• cosec (90° – θ) = sec θ

Supplementary Angles Identities

• sin (180°- θ) = sinθ
• cos (180°- θ) = -cos θ
• cosec (180°- θ) = cosec θ
• sec (180°- θ)= -sec θ
• tan (180°- θ) = -tan θ
• cot (180°- θ) = -cot θ

Periodicity of Trigonometric Ratios

• sin (2nπ + θ) = sin θ
• cos (2nπ + θ) = cos θ
• tan (nπ + θ) = tan θ 
• cosec (2nπ + θ) = cosec θ
• sec (2nπ + θ) = sec θ
• cot (nπ + θ) = cot θ

Angle Sum and Difference Formulas

List of angle sum and difference formulas is give as follows:

• 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) ​

Read more about Sum and Difference Formulas.

Product to Sum Formulas

List of formulas for converting the product of two trigonometric functions into the sum or difference of two trigonometric functions is given as follows:

• sin(A) sin(B) = 1/2 ​[cos(A−B) − cos(A+B)]
• cos(A) cos(B) = 1/2 ​[cos(A−B) + cos(A+B)]

Some other related identities are:

• sin(A+B) sin(A–B) = sin²A–sin²B=cos²B–cos²A
• cos(A+B) cos(A–B)=cos²A–sin²B=cos²B–sin²A
• sinA+sinB = 2 sin (A+B)/2 cos (A-B)/2

Read More about Product to Sum Formulas.

Twice Angle Formulas

Identities containing double angle are:

• sin (2θ) =2sin(θ)cos(θ) = [2tan θ /(1+tan²θ)]
• cos⁡(2θ)=cos⁡²(θ)−sin^⁡2(θ) = 1–2sin²θ = 2cos²θ–1 = [(1-tan²θ)/(1+tan²θ)]
• tan⁡(2θ)=2tan⁡(θ) / 1−tan⁡²(θ)

Read More about Sin 2x Formula.

Half Angle Formulas

Half-angle formulas are derived by replacing 2x with x/2 in double-angle identities, resulting in the following identities:

• [Tex]\sin\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 – \cos(\theta)}{2}}[/Tex]
• [Tex]\cos\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 + \cos(\theta)}{2}}[/Tex]
• [Tex]\tan\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1 – \cos(\theta)}{1 + \cos(\theta)}}[/Tex]

Thrice Angle Formulas

Trigonometric Formulas containing three time multiple of any angle θ is given as:

• sin 3θ = 3sinθ – 4sin³θ
• cos 3θ = 4cos³θ – 3cosθ
• tan 3θ = [3tanθ–tan³θ]/[1−3tan²θ]

Trigonometric Formulas are mathematical expressions that relate the angles and sides of triangles. These formulas help in solving problems related to angles, distances, and heights in various geometric and real-world scenarios. In this article we will learn about the different trigonometric formulas of class 11 level and at the last of this we will also solve some example for better understanding.