Class 10 Exam  >  Class 10 Questions  >  If cosec a cot a is equal to m then prove t... Start Learning for Free
If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta?
Most Upvoted Answer
If cosec a cot a is equal to m then prove that m square minus 1 / m ...
If cosec a cot a = m, prove that (m^2 - 1)/(m^2 + 1) = cos^2(a) - sin^2(a).

Proof:

To prove that (m^2 - 1)/(m^2 + 1) = cos^2(a) - sin^2(a), let's start by expressing cosec a and cot a in terms of sin a and cos a.

Expressing cosec a and cot a in terms of sin a and cos a:

Using the definitions of cosec a and cot a, we have:

cosec a = 1/sin a
cot a = cos a/sin a

Substituting the expressions of cosec a and cot a:

Now, substituting the values of cosec a and cot a in the given equation m = cosec a cot a, we get:

m = (1/sin a) * (cos a/sin a)

Simplifying the expression:

m = cos a/sin^2 a

Squaring both sides of the equation:

Now, let's square both sides of the equation m = cos a/sin^2 a to eliminate the square in the denominator:

m^2 = (cos^2 a)/(sin^4 a)

Using the identity sin^2 a + cos^2 a = 1:

We know that sin^2 a + cos^2 a = 1. Rearranging the equation, we get:

sin^2 a = 1 - cos^2 a

Substituting this expression in the equation m^2 = (cos^2 a)/(sin^4 a), we get:

m^2 = cos^2 a/(1 - cos^2 a)^2

Expanding the denominator:

Expanding the denominator (1 - cos^2 a)^2, we get:

m^2 = cos^2 a/(1 - 2cos^2 a + cos^4 a)

Simplifying the expression:

To simplify the expression further, we can use the identity cos^2 a = 1 - sin^2 a. Substituting this in the equation, we get:

m^2 = (1 - sin^2 a)/(1 - 2(1 - sin^2 a) + (1 - sin^2 a)^2)

Simplifying the expression:

m^2 = (1 - sin^2 a)/(1 - 2 + 2sin^2 a - sin^4 a)

m^2 = (1 - sin^2 a)/(3 - 2sin^2 a + sin^4 a)

Using the identity sin^2 a + cos^2 a = 1:

We know that sin^2 a + cos^2 a = 1. Rearranging the equation, we get:

cos^2 a = 1 - sin^2 a

Substituting this expression in the equation m^2 = (1 - sin^2 a)/(3 - 2sin^2 a + sin^4 a), we get:

m^2 = cos^2 a/(3 - 2sin^2 a + sin^4 a)

Using the identity cos^2
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

Top Courses for Class 10

If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta?
Question Description
If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta? 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 If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta?.
Solutions for If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta? 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 If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta? defined & explained in the simplest way possible. Besides giving the explanation of If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta?, a detailed solution for If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta? has been provided alongside types of If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta? theory, EduRev gives you an ample number of questions to practice If cosec a cot a is equal to m then prove that m square minus 1 / m square 1 is equal to cos theta? tests, examples and also practice Class 10 tests.
Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev