Proof : Cosec^2 x - Cot^2 x =1 | [ TRIGONOMETRY ]

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In this video, we will prove that Cosec^2 x - Cot^2 x = 1, it is a very important
identity in trigonometry and also one of the most useful ones.

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Topics discussed in this video :

1. Value of Cot x and Cosec x ,wih respect to a given triangle.
2. Pythagoras Theorem
3. sin^2 x + Cos^2 x =1

How to prove that Cosec^2 x - Cot^2 x =1 :

------------------------------------METHOD 1--------------------------

1. Take any right-angle triangle.
2, substitute the value of Cosec x and Cot x in the video.
3. Then we will take the l.c.m of the two fractions.
4. after that we will get h^2 - b^2 in the numerator and p^2 in the denominator.
5. Then we can use the Pythagoras theorem to substitute the value of h^2 - b^2 as p^2
6. Finally we will get the value as 1.

--------------------------------METHOD 2------------------------------------

1. convert cosec x and cotx in terms of sinx and cosx
2. Then after taking the lcm we will get
3. Then we will have 1 - sin^2 x in the numerator and cos^x in the denominator.
4. since they both are equal they will get cancelled and we will get our ans as 1

lectures on properties of the triangle:

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Is there any other method except these two??

ravipathak