Class 10 Exam > Class 10 Questions > Prove that cosec²A-cos²A/ cot²A = sec²A - sin...
Start Learning for Free
Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A?
Most Upvoted Answer
Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A?
Community Answer
Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A?
Proof of cosec²A-cos²A/ cot²A = sec²A - sin²A
Step 1: Convert cot²A to cos²A/ sin²A
To simplify the left side of the equation, we need to convert cot²A to cos²A/ sin²A:
cosec²A - cos²A/ cot²A = cosec²A - cos²A/(cos²A/ sin²A) = cosec²A - sin²A
Step 2: Convert sec²A to 1/cos²A
To simplify the right side of the equation, we need to convert sec²A to 1/cos²A:
sec²A - sin²A = 1/cos²A - sin²A
Step 3: Convert sin²A to 1 - cos²A
To further simplify the right side of the equation, we need to convert sin²A to 1 - cos²A:
1/cos²A - sin²A = 1/cos²A - (1 - cos²A) = 1/cos²A - 1 + cos²A
Step 4: Combine like terms on the right side of the equation
To simplify the right side of the equation further, we need to combine like terms:
1/cos²A - 1 + cos²A = (1 - cos²A + cos⁴A)/cos²A
Step 5: Simplify the right side of the equation
To simplify the right side of the equation even further, we need to factor the numerator of the fraction:
(1 - cos²A + cos⁴A) = (1 - cos²A)(1 + cos²A) = sin²A/cos²A * (1 + cos²A) = sin²A + sin²A cos²A/cos²A = sin²A + sin²A = 2sin²A
Step 6: Simplify the left side of the equation
Now that we have simplified the right side of the equation, we can simplify the left side of the equation using the result from Step 1:
cosec²A - sin²A = (1/sin²A) - sin²A = (1 - sin⁴A)/sin²A = (1 - sin²A)(1 + sin²A)/sin²A = cos²A/sin²A = 1/cos²A
Step 7: Compare the simplified left and right sides of the equation
Now that we have simplified both sides of the equation, we can compare them:
1/cos²A = 1/cos²A
Therefore, we have proved that cosec²A-cos²A/ cot²A = sec²A - sin²A.
Step 1: Convert cot²A to cos²A/ sin²A
To simplify the left side of the equation, we need to convert cot²A to cos²A/ sin²A:
cosec²A - cos²A/ cot²A = cosec²A - cos²A/(cos²A/ sin²A) = cosec²A - sin²A
Step 2: Convert sec²A to 1/cos²A
To simplify the right side of the equation, we need to convert sec²A to 1/cos²A:
sec²A - sin²A = 1/cos²A - sin²A
Step 3: Convert sin²A to 1 - cos²A
To further simplify the right side of the equation, we need to convert sin²A to 1 - cos²A:
1/cos²A - sin²A = 1/cos²A - (1 - cos²A) = 1/cos²A - 1 + cos²A
Step 4: Combine like terms on the right side of the equation
To simplify the right side of the equation further, we need to combine like terms:
1/cos²A - 1 + cos²A = (1 - cos²A + cos⁴A)/cos²A
Step 5: Simplify the right side of the equation
To simplify the right side of the equation even further, we need to factor the numerator of the fraction:
(1 - cos²A + cos⁴A) = (1 - cos²A)(1 + cos²A) = sin²A/cos²A * (1 + cos²A) = sin²A + sin²A cos²A/cos²A = sin²A + sin²A = 2sin²A
Step 6: Simplify the left side of the equation
Now that we have simplified the right side of the equation, we can simplify the left side of the equation using the result from Step 1:
cosec²A - sin²A = (1/sin²A) - sin²A = (1 - sin⁴A)/sin²A = (1 - sin²A)(1 + sin²A)/sin²A = cos²A/sin²A = 1/cos²A
Step 7: Compare the simplified left and right sides of the equation
Now that we have simplified both sides of the equation, we can compare them:
1/cos²A = 1/cos²A
Therefore, we have proved that cosec²A-cos²A/ cot²A = sec²A - sin²A.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A?
Question Description
Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A?.
Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A?.
Solutions for Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? defined & explained in the simplest way possible. Besides giving the explanation of
Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A?, a detailed solution for Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? has been provided alongside types of Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? theory, EduRev gives you an
ample number of questions to practice Prove that cosec²A-cos²A/ cot²A = sec²A - sin²A? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup