 # Trigonometry Formulas For Class 11

Trigonometry is a branch of mathematics which studies the relationships between angles and lengths of triangles. It is a very important topic of mathematics just like statistics, linear algebra and calculus. In addition to mathematics, it also contributes majorly to engineering, physics, astronomy and architectural design. Trigonometry Formulas for class 11 play a crucial role in solving any problem related to this chapter. Also, check Trigonometry For Class 11 where students can learn notes, as per the CBSE syllabus and prepare for the exam.

## List of Class 11 Trigonometry Formulas

Here is the list of formulas for Class 11 students as per the NCERT curriculum. All the formulas of trigonometry chapter are provided here for students to help them solve problems quickly.

 Trigonometry Formulas sin(−θ) = −sin θ cos(−θ) = cos θ tan(−θ) = −tan θ cosec(−θ) = −cosecθ sec(−θ) = sec θ cot(−θ) = −cot θ Product to Sum Formulas sin x sin y = 1/2 [cos(x–y) − cos(x+y)] cos x cos y = 1/2[cos(x–y) + cos(x+y)] sin x cos y = 1/2[sin(x+y) + sin(x−y)] cos x sin y = 1/2[sin(x+y) – sin(x−y)] Sum to Product Formulas sin x + sin y = 2 sin [(x+y)/2] cos [(x-y)/2] sin x – sin y = 2 cos [(x+y)/2] sin [(x-y)/2] cos x + cos y = 2 cos [(x+y)/2] cos [(x-y)/2] cos x – cos y = -2 sin [(x+y)/2] sin [(x-y)/2] Identities sin2 A + cos2 A = 1 1+tan2 A = sec2 A 1+cot2 A = cosec2 A

### Sign of Trigonometric Functions in Different Quadrants

 Quadrants→ I II III IV Sin A + + – – Cos A + – – + Tan A + – + – Cot A + – + – Sec A + – – + Cosec A + + – –

### Basic Trigonometric Formulas for Class 11

cos (A + B) = cos A cos B – sin A sin B

cos (A – B) = cos A cos B + sin A sin B

sin (A+B) = sin A cos B + cos A sin B

sin (A -B) = sin A cos B – cos A sin B

Based on the above addition formulas for sin and cos, we get the following below formulas:

• sin(π/2-A) = cos A
• cos(π/2-A) = sin A
• sin(π-A) = sin A
• cos(π-A) = -cos A
• sin(π+A)=-sin A
• cos(π+A)=-cos A
• sin(2π-A) = -sin A
• cos(2π-A) = cos A

If none of the angles A, B and (A ± B) is an odd multiple of π/2, then

• tan(A+B) = [(tan tan B)/(– tan tan B)]
• tan(A-B) = [(tan A – tan B)/(1 + tan tan B)]

If none of the angles A, B and (A ± B) is a multiple of π, then

• cot(A+B= [(coco− 1)/(cocoA)]
• cot(A-B= [(cocoB + 1)/(coB – coA)]

Some additional formulas for sum and product of angles:

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

Formulas for twice of the angles:

• sin2A = 2sinA cosA = [2tan A /(1+tan2A)]
• cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]
• tan 2A = (2 tan A)/(1-tan2A)

Formulas for thrice of the angles:

• sin3A = 3sinA – 4sin3A
• cos3A = 4cos3A – 3cosA
• tan3A = [3tanA–tan3A]/[1−3tan2A]

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