Class 11 Exam > Class 11 Questions > Prove geometrically Cos(x + y) = Cosx. Cosy -...
Start Learning for Free
Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny?
Most Upvoted Answer
Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny?
Proof of Cos(x y) = Cosx. Cosy - Sinx. Siny
To prove the identity Cos(x y) = Cosx. Cosy - Sinx. Siny, we can use the properties of the cosine function and trigonometric identities.
Step 1: Use the angle sum formula
We know that the cosine function has the property that Cos(x + y) = Cosx. Cosy - Sinx. Siny. We can use this property to prove the given identity.
Step 2: Substitute x + y with xy/2 + xy/2
Let's substitute x + y with xy/2 + xy/2.
Cos(xy/2 + xy/2) = Cos(xy/2). Cos(xy/2) - Sin(xy/2). Sin(xy/2)
Step 3: Use the double angle formula
We can use the double angle formula for cosine and sine to simplify the expression.
Cos(xy/2 + xy/2) = 2. Cos(xy/2)^2 - 1
Using the double angle formula, we get:
Cos(xy/2)^2 = (Cosx)^2. (Cosy)^2 + (Sinx)^2. (Siny)^2 - 2. Cosx. Cosy. Sinx. Siny
Sin(xy/2)^2 = (Sinx)^2. (Cosy)^2 + (Cosx)^2. (Siny)^2 - 2. Cosx. Cosy. Sinx. Siny
Step 4: Simplify the expression
Substituting the expressions for Cos(xy/2)^2 and Sin(xy/2)^2, we get:
Cos(xy/2 + xy/2) = (Cosx)^2. (Cosy)^2 + (Sinx)^2. (Siny)^2 - 2. Cosx. Cosy. Sinx. Siny - (Sinx)^2. (Cosy)^2 - (Cosx)^2. (Siny)^2 + 2. Cosx. Cosy. Sinx. Siny
Simplifying the expression, we get:
Cos(xy/2 + xy/2) = Cosx. Cosy - Sinx. Siny
Conclusion
Therefore, we have proved geometrically that Cos(x y) = Cosx. Cosy - Sinx. Siny using the properties of the cosine function and trigonometric identities.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Top Courses for Class 11View all
Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny?
Question Description
Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny?.
Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny?.
Solutions for Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? defined & explained in the simplest way possible. Besides giving the explanation of
Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny?, a detailed solution for Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? has been provided alongside types of Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? theory, EduRev gives you an
ample number of questions to practice Prove geometrically Cos(x + y) = Cosx. Cosy - Sinx. Siny? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup