Dear readers, in this article I provide all Trigonometry Formulae for all students, aspirants for competitive examination. You can read also an important **List of Chemical Names and formulas: All common Formulas **for all competitive examinations like Railway, SSC, Banking, IAS, State PSU, etc.

Table of Contents

## All Basic Trigonometry Formulae are:-

**In a Right-angled Triangle,**

**Hypotenuse-h**

**Perpendicular-p**

**Base-b**

**Hypotenuse:** The longest side of the triangle which in front of the right angle(90^{0}).

**Perpendicular:** The side making an angle of 90 degrees with the Base.

**Base:** The side that is horizontal to the plane.

__Trigonometry Formulae: Pythagoras Theorem__

__Trigonometry Formulae: Pythagoras Theorem__

In ABC Δ ,**AB ^{2} + BC^{2 }= AC^{2}**

**h ^{2} = p^{2} + b^{2}**

**h = ****√****p ^{2} + b^{2}**

**p ^{2} = h^{2 }– b^{2}**

**p = ****√****h ^{2 }– b^{2}**

**b ^{2 }= h^{2} -p^{2} **

**b = ****√****h ^{2} -p^{2} **

There are basically** 6** **Ratios in Trigonometry to find the elements in Trigonometry****:-**sine, cosine, tangent, cotangent, secant, cosecant. Generally, we read as **Sin, cos, tan, cot, sec, and cosec.**

__Relations among trigonometrial ratios__

__Relations among trigonometrial ratios__

**sin θ = Perpendicular /Hypotenuse =p/h****cos θ = Base /Hypotenuse =b/h****tan θ = Perpendicular/ Base =p/b****cot θ = Base /Perpendicular = b/p****sec θ = Hypotenuse/ Base =h/b****cosec θ = Hypotenuse/ Perpendicular =h/p**

__Sine and Cosine Law Trigonometry Formulae__

__Sine and Cosine Law Trigonometry Formulae__

The Sine and Cosine Law gives a relationship between the sides and angles of a triangle.

**Sine Law:-**

The Sine Law gives the ratio of the sides and the angle opposite to the side. The ratio is taken for the side ‘a’ and its opposite angle ‘A’.

** **

**Cosine Law:-**

The Cosine Law helps to find the length of a side, for the given lengths of the other two sides and the included angle.

The length ‘a’ can be found with the help of the other two sides ‘b’ and ‘c’ and their included angle ‘A’.

**a**^{2}=b^{2}+c^{2}−2bc Cos A**,****b**^{2}=a^{2}+c^{2}−2ac Cos B**,****c**^{2}=a^{2}+b^{2}−2ab Cos C**.**

__Reciprocal Relations:__

__Reciprocal Relations:__

__Square Relations in Trigonometry Formulae:__

__Square Relations in Trigonometry Formulae:__

**sin**^{2}θ + cos^{2}θ = 1**sec**^{2}θ – tan^{2 }θ = 1**cosec**^{2}θ – cot^{2 }θ = 1**sin**^{2}θ= 1- cos^{2}θ**cos**^{2}θ = 1 – sin^{2}θ**sec**^{2}θ = 1 + tan^{2 }θ**tan**^{2 }θ = sec^{2}θ -1**cosec**^{2}θ = 1 + cot^{2 }θ**cot**^{2 }θ = cosec^{2}θ -1

__Quotient Relations in Trigonometry Formulae:__

__Quotient Relations in Trigonometry Formulae:__

__Trigonometric Functions Of Sum And Difference Of Two Angles__

__Trigonometric Functions Of Sum And Difference Of Two Angles__

__Trigonometrical ratios of compound angles__

__Trigonometrical ratios of compound angles__

**sin (A+B)= sin A. cos B + cos A. sin B****sin (A−B)= sin A. cos B – cos A. sin B****cos (A+B)= cos A.cos B – sin A. sin B****cos (A−B)= cos A.cos B + sin A. sin B**

**sin (A + B) + sin (A – B) = 2 sin A . cos B****sin (A + B) – sin (A – B) = 2 cos A . sin B****cos (A + B) + cos (A – B) = 2 cos A . cos B****cos (A – B) – cos (A + B) = 2 sin A . sin B**

** **

**sin (A + B) . sin (A – B) = sin**^{2}A – sin^{2}B = cos^{2}B – cos^{2}A**cos (A + B) . cos (A – B) = cos**^{2}A – sin^{2}B = cos^{2}B – sin^{2}A

__Sum to Product Identities__

__Product identities__

__Double Angle Formulas __

__Double Angle Formulas__

**Sin 2A = 2 sin A .cos A =****tan A/1+****tan**^{2}A**Cos 2A = cos**^{2}A − sin^{2}A

**Cos 2A = = 2 cos**^{2}θ − 1**Cos 2A = = 1 − 2 sin**^{2}θ

**tan 2A= 2 tan A /1 − tan**^{2}A**cot 2A=cot**^{2}A-1/2cotA

**1 + Sin 2A = (cosA + sinA)**^{2}**1 – Sin 2A = (cosA – sinA)**^{2}**1+cos 2A= 2cos**^{2}A**1-cos 2A= 2sin**^{2}A

__Half Angle Formula in Trigonometry __

__Half Angle Formula in Trigonometry__

__Co-function Identities (in Degrees) ____(0__^{0 } < θ < 90^{0})

^{0 }< θ < 90

^{0})

**sin (****90**^{0 }– θ )=**cos****θ****cos (****90**^{0 }– θ )=**sin****θ****tan (****90**^{0 }– θ ) =**cot****θ****cot (****90**^{0 }– θ ) =**tan****θ****sec (****90**^{0 }– θ )=**cosec****θ****cosec (****90**^{0 }– θ ) =**sec****θ**

__90__^{0 } < θ < 180^{0}

__90__

^{0 }< θ < 180^{0}

**sin (****90**^{0}+θ ) =**cos****θ****cos (****90**^{0 }+θ )= –**sin****θ****tan (****90**^{0 }+θ ) = –**cot****θ****cot (****90**^{0 }+θ ) = –**tan****θ****sec (****90**^{0 }+θ )= -co**sec****θ****cosec (****90**^{0 }+ θ ) =**sec****θ**

**0**^{0 }< θ < 180^{0}

^{0 }< θ < 180

^{0}

**sin (****180 ^{0}-θ )= **

**sin**

**θ**

**cos (****180 ^{0}-θ )=-**

**cos**

**θ**

**tan (****180 ^{0}-θ ) = – **

**tan**

**θ**

**cot (****180 ^{0}-θ ) = –**

**cot**

**θ**

**sec (****180 ^{0}-θ )= –**

**sec**

**θ**

**cosec (****180 ^{0}– θ ) = **

**cosec**

**θ**

__Trigonometric Table Value__

__Trigonometric Table Value__