# Basic Trigonometric Identities with Proof

#### Trigonometric Identities for class 10 , 11 & Higher

BASIC TRIGONOMETRY IDENTITIES : We have already studied the Trigonometry meaning, What is meant by Trigonometry actually in our “Trig Course Part 1“. In this post, we provide all basic trigonometric Formulae with proof in simplest method with tricks. All these basic trigonometry formulae are most important for Class 10 chapter 8 maths , trigonometry functions class 11 etc. Before starting this, please read our 1st part if you didn’t read –

## Trigonometric Formulae List 2

From the first table, you can see that sin and cosec are reciprocal (Multiplicative inverse) to each other. Simillarly, tan & cot , also cos and sec are also reciprocals to each other. We know that, product of any two number which are reciprocal to each other, is 1. So, We can get the following identities:-

• SinA . CosecA = 1
• CosA . SecA = 1
• TanA . CotA = 1

Thus we can get the bellow trig identities table, all these identities are most important to prove other dependent trigonometric formula, specially for Trigonometry Identities Class 10, Trigonometric Identities class 11 and for higher educations.. To remember the above trigonometric identities table , we just need to study the first trig identities list. If you have studied the first table carefully, you can also create these trigonometric formula by yourself.

## Basic Trigonometric Identities Table – 3 Firstly, to proof these identities, we just have to know the Trigonometric Identities List 1. From the first table, we have studied that, the ratio of Perpendicular (P) and the Hypotenuse (H) is the Sin and that of Base(B) and Hypotenuse (H) is Cos. We also study that the ratio of Perpendicular and Base is Tan.

So, We can write,

sinA/cosA = (P/H) / (B/H) = P / B = tanA

Which is the first identity from the table – 3

Simillarly, We can prove all these 4 identity as follows: ## 3 SPECIAL TRIGONOMETRIC FORMULAE:

 (i) Sin²A + Cos²A = 1 (ii) 1 + Tan²A = Sec²A (iii) 1 + Cot²A = Cosec²A

These three trigonometric formulae are most important three identities from trigonometry which are being used to proof and solve lots of mathematical phenomena & problems. We can prove them using the Pythagoras theorem bellow: From Pythagoras Theorem, For any right angular triangle, we get–

(Perpendicular)² + (Base)²  = (Hypotenuse)²  So, these three basic trigonometry formulas (formulae) are also the primary identities of trigonometry. Hope, your all confusion has cleared.  If no, please comment bellow with your query about the basic trigonometry identities and their proof. After all, You can also download these three lists with proof, means trigonometric identities pdf file from bellow section. 