# Trigonometric Formula & Equations: Notes for JEE 2020

JEE Main Short Notes

By Poojashree AgarwalUpdated : Sep 10, 2020 , 19:04 IST

The basic formulas of Trigonometry are no doubt one of the essential to study topics in mathematics. Considering its importance, in exams such as JEE Main / JEE Advanced there are about 4-5 questions asked directly from the topic alongside some questions in which trigonometry is imbibed into questions asked from some other topic. Thoroughly revise all the important formulas by downloading the Trigonometric ratios and equations notes pdf from the link given below.

## 2. Trigonometric Identities

a) sin2 θ + cos2 θ = 1

b) sec2 θ = 1 + tan2 θ

c) cosec2 θ = 1 + cot2 θ

## 4. Trigonometric Ratios for compound Angles

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

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

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

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

e) tan (A + B) =

f) tan (A – B) =

g) cot (A + B) =

h) cot (A – B) =

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

j) cos (A + B + C) = cos A cos B cos C – cos A sin B sin C - sin A cos B sin C – sin A sinBcos C

k) tan ( A + B + C) =

## 5. Transformation Formula (product into sum or difference)

a) 2 sin A cos B = sin (A + B) 8 sin (A – B)

b) 2 cos A sin B = sin (A + B) – sin (A – B)

c) 2 cos A cos B = cos (A + B) + cos (A – B)

d) 2 sin A sin B = cos (A – B) – cos (A + B)

## 6. Transformation Formula (sum or difference into product)

a) sin C + sin D =

b) sin C – sin D =

c) cos C + cos D =

d) cos D – cos C =

## 7. Trigonometric Ratios of Multiple angles

a) cos 2 A = cos2 A – sin2 A = 1 – 2 sin2 A = 2 cos2 A – 1=

b) sin 2 A = 2 sin A cos A =

c) tan 2 A =

d) sin 3 A = 3 sin3 A – 4 sin3 A

e) cos 3 A = 4 cos3 A – 3 cos A

f) tan 3 A =

g) tan (A1 + A2 + ……..+ An) =

where

S1 = sum of tangents of angles taken one at a time

S2 = sum of product of tangents of angles taken two at a time

And so on

Sn = sum product of tangents of angles taken n at a time

## 8. Sum of sines or cosines of n angles in A.P.

a) sin A + sin (A + B) + sin (A + 2B) +……..+ sin (A + (n-1)B) =

b) cos A + cos (A + B) + cos ( A + 2B) +……….+ cos (A + (n-1)B) =

## 9. General solution of elementary Trigonometric equations

a) sin θ = 0 ⇒ θ = n π

b) tan θ = 0 ⇒ θ = n π

c) cos θ = 0 ⇒ θ = (2n + 1) π/2

d) sin θ = 1 ⇒ θ = (4n + 1) π/2

e) cos θ = - 1 ⇒ θ = (4n – 1) π/2

f) cos θ = 1 ⇒ θ = 2n π

g) cos = - 1 ⇒ θ = (2n + 1) π

h) cot θ = 0 ⇒ θ (2n + 1) π/2

## 10. General solution of some standard equations

a) sin θ = sin α ⇒ θ = nπ + (-1)n θ

b) cos θ = cos α ⇒ θ = 2nπ ± θ

c) tan θ = tan α ⇒ θ = nπ +θ

## 11. Solution of equations of the form A cos θ + B sin θ = C

Step 1: check whether  , if in equality is true move to step 1 otherwise the equation has no solution

Step 2: Multiply both sides of equation by

Now you may take either

Sin α =  , then cos α =

Or

sin α =, then cos α =

Thus the equation either reduces to a form cos (θ – α) = cos β or sin (θ + α) = sin β.

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Class 12thChemistryMathsPhysics

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Poojashree Agarwal

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