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
P- Perpendicular H- Hypotenuse B – Base
L – लम्ब A – आधार K – कर्ण
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
| θ | 0° | 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
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