# Short Tricks of Trigonometry, Notes & Formula Sheet PDF – 7tricks

Today we talk about a very important and high weightage chapter Trigonometry. Also, you get here Short notes of Trignometry and an all-important formulas sheet for it! this will definitely help you in competitive exams like JEE, NDA, Bitsat, Ntse, SSC-CGL, CHSL etc.

First of all, we talk about basic formulas and identities of trigonometry:-

#### 1) Trigonometric Ratios:-

sinθ = P/H or L/K   cosθ = B/H or A/K

tanθ = P/B or L/A   cotθ = B/P or L/A

secθ = H/B or K/A  cosecθ = H/P or K/L

Here
P- Perpendicular H- Hypotenuse B – Base
L – लम्ब  A – आधार K – कर्ण
•▶ Always remember Perpendicular side is in front of the angle(θ).

Trick to learn-
For English:- PBP/HHB [Pandit Badri Prasad Har Har Bole]
For Hindi:- LAL/KKA [लाल/ कक्का]

#### 2) Pythagorean Identities:-

sin²θ + cos²θ = 1
1 + tan²θ  = sec²θ
1 + cot²θ  = cosec²θ

#### 3) Trignometric Ratio Table

Table
θ 30° 45° 60° 90°
sinθ 0 1/2 1/√2 √3/2 1
cosθ 1 √3/2 1/√2 1/2 0
tanθ 0 1/√3 1 √3
cotθ √3 1 1/√3 0
secθ 1 2/√3 √2 2
cosecθ 2 √2 2/√3 1

#### 4) If X + Y = 90° then,

a) sin X. sec Y = 1 or  sin X = cos Y
b) cos X. cosec Y = 1 or  sec X = cosec Y
c) tan X. tan Y = 1  or tan X = cot Y
d) cos² X + cos² Y = 1
e) sin²X + sin² Y = 1
f) cot X. cot Y = 1

#### 5) Trignomertry Formula of sum and difference

a) sin (X+Y) =sinX. cosY + cosX sinY
b) sin(X – Y) =sinX. cosY – cosX sinY
c) cos(X+Y) =cosX. cosY – sinX sinY
d) cos(X-Y) = cosX. cosY+sinX sinY
e) 2 sinX.cosY = sin(X+Y)+sin (X-Y)
f) 2 cosX. sinY = sin(X+Y)-sin (X-Y)
g) 2 sinX. sinY = cos(X-Y)-cos(X+Y)
h) 2 cosX.cosY = cos(X+Y)+cos(X-Y)
i) sin²X-sin²Y = sin(X+Y). sin(X-Y)
j) cos²X-cos²Y = cos(X+Y).cos (X-Y)

#### 6) Some results in Trigonometry:

a) If X + Y + Z = 180° Then,
tan X + tan Y + tan Z = tan X. tan Y. tan Z
b) If X + Y + Z = 90° Then,
cot X + cot Y + cot Z = cot X cot Y cot Z