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(θtan θ
cosec(θcosecθ
sec(θsec θ
cot(θcot 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 cos 1/2[sin(x+ysin(xy)]
cos sin 1/2[sin(x+y– sin(xy)]
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]

Also check:

20 Comments

  1. Only want useful formula of PCM

    1. these all are useful formula of PCM

  2. thankyou so much byjus, your quick notes of formulaes helped me alot, thnx again

  3. It’s good thanks byjus

  4. Very useful notes, thanks byjus

  5. Thank you Byju’s. It is very helpful to me

  6. Thanks, guys for making our work easier and a lot more comfortable by posting all the formulas together in one place in a systematic manner

  7. Thank you Byjus. It was really helpful

  8. these are not all

  9. Thanks bijus for the list of formulas

  10. hey how to overcome the fear of phy and chem

  11. Thank you byju’s your list of formula helped me a lot thankx alot

  12. Thanks but if u keep derivation it will be so useful to others and they will not have any confusion but thanx for this

  13. VERY COOL!!!!!!!

  14. THANK YOU SO MUCH BYJUS FOR MAKING OUR WORK EASY AND SIMPLE

  15. Thank you so much

  16. i would like the list of the trignometric identities for class 11

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