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

Trigonometry short tricks

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

How to download: 
Just click on ‘Download Notes PDF’ in the green button then a page will open that contains these short notes on google drive. Wait for 30 seconds and after that click on download image. You can see them on that page or you can download them (the download button will be on the top right corner.)
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