**Basic Identities of Trigonometry**

Trigonometry is the important topic among the competitive exam like RRB NTPC Second Stage exam and SSC CGL Tier I and Tier II questions. In RRB NTPC Exam, they are asked only simple question, why we say it simple, because we could solve by the way of applying the basic trigonometry formulas. Let we, try to memories it

**(i) ****Sec ^{2}θ^{ }= tan^{2}θ^{ }= 1**

** (Secθ ^{ }- tanθ^{ }) (Secθ^{ }+ tanθ^{ }) = 1**

**If Secθ ^{ }± tanθ = x then, Secθ^{ }± tanθ = 1/x**

**(ii) Cosec ^{2}θ – Cot^{2}θ ^{ }= 1**

**(Cosecθ – Cotθ ) (Cosecθ + Cotθ ) = 1**

** If Cosecθ ± Cotθ = x then Cosecθ ± Cotθ = 1/x**

**(iii) Sin ^{2}θ + Cos^{2}θ = 1,**

** ****Sin ^{2}θ = 1- Cos^{2}θ,**

** ****Cos ^{2}θ =1 - Sin^{2}θ,**

**(iv) Sec ^{2}θ - tan^{2}θ = 1,**

** Sec ^{2}θ =1 + tan^{2}θ,**

** tan ^{2}θ = Sec^{2}θ - 1,**

**(v) Cosec ^{2}θ - Cot^{2}θ ^{ }= 1,**

** Cosec ^{2}θ = 1 + Cot^{2}θ,**

** Cot ^{2}θ ^{ }= Cosec2θ - 1,**

**(vi) If Sinθ + Cosθ = 0 then, **

**Sinθ - Cosθ - √2-θ ^{2}**

**(vii) Cos ^{2 }θ = 1/2 (1+Cos 2θ)**

** Sin ^{2} θ = 1/2 (1-Cos 2θ) **

**(viii) tan A = Sin A/ Cos A**

** tan ( A ±** **B) = tan A ± tan B / 1 ± tan A tan B**

**(ix) Sin(2A) = 2 Sin A Cos A**

** Cos(2A) = Cos ^{2} A - Sin^{2} A**