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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:
Ace In Academy is a start-up by Shivam Pasari to Provide the best quality lectures on all the fields of maths from class 6 to university level and for any competitive exam and olympiad.
Subscribe to Ace In Academy Youtube channel to get access to high-level videos on all mathematical concepts.
Whatsapp group link for CAT preparation:
#maths
#proof
#trigonometry
identity in trigonometry and also one of the most useful ones.
[ SUBSCRIBE OUR YOUTUBE CHANNEL ]
👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇
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:
Ace In Academy is a start-up by Shivam Pasari to Provide the best quality lectures on all the fields of maths from class 6 to university level and for any competitive exam and olympiad.
Subscribe to Ace In Academy Youtube channel to get access to high-level videos on all mathematical concepts.
Whatsapp group link for CAT preparation:
#maths
#proof
#trigonometry
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