Trigonometric Ratios & Proves

Some Important points before we start our proves .

  1. We should know the naming of sides of a right angle triangle click here to understand it .
  2. Pythagoras Theorem “In a Right angled Triangle square of Hypotenuse will be SUM of square of each other sides  .” i.e Hypotenuse2 =Base2+Perpendicular2

If we take 3-4 right angle triangles having same angle ϑ that means there all triangles having a common angle and then if we calculate the ratios of sides for each different triangles like perpendicular/Hypotenuse , Base/Hypotenuse and perpendicular/base and inverse of all these .

Then we will find that each same ratios from different triangles in respect to common angle ϑ are same .

So we can easily assume that for each triangle perpendicular/Hypotenuse , Base/Hypotenuse and perpendicular/base are same in respect with angle ϑ.

So we can assume any constant for such values and which will depends on ϑ.

Mathematicians assumes SIN as Ratio of perpendicular/Hypotenuse then

Sin ϑ= perpendicular/Hypotenuse and in similar way they assumes Cosϑ=Base/Hypotenuse  and tanϑ=perpendicular/base

So we have ;

Sin ϑ= perpendicular/Hypotenuse




Inverse of Above Ratios:

Cosecϑ= Hypotenuse/perpendicular



To-remember these value we use a name :

pandit badri prasad har har bole and to represent these all trigonometric ratios we can arrange this like below

pandit badri prasad / har har bole

If we take all words first latter then it will become


P will represent Perpendicular , B base and h Hypotenuse .

And if we take it from up to down we will have sin=>P/H , Cos=>B/H => and Tan => P/B and if we take down to up we will have all inverse ratios cosec=>H/P,Sec=>H/B and cot=>B/P.


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