Class 10 Exam > Class 10 Questions > If cosA cos2A = 1 then the value of sin2A ...
Start Learning for Free
If cosA cos2A = 1 then the value of sin2A sin4A is?
Most Upvoted Answer
If cosA cos2A = 1 then the value of sin2A sin4A is?
Community Answer
If cosA cos2A = 1 then the value of sin2A sin4A is?
Cosine Double Angle Formula:
The cosine double angle formula states that cos(2A) = 2cos^2(A) - 1.
Given:
cos(A) * cos(2A) = 1
Using the Cosine Double Angle Formula:
cos(2A) = 2cos^2(A) - 1
Substituting the given equation:
cos(A) * (2cos^2(A) - 1) = 1
Simplifying the equation:
2cos^3(A) - cos(A) = 1
Factoring out cos(A):
cos(A)(2cos^2(A) - 1) = 1
Dividing both sides by 2cos^2(A) - 1:
cos(A) = 1 / (2cos^2(A) - 1)
Using the Pythagorean Identity:
cos^2(A) + sin^2(A) = 1
Solving for sin^2(A):
sin^2(A) = 1 - cos^2(A)
Substituting into the equation:
cos(A) = 1 / (2(1 - sin^2(A)) - 1)
Simplifying the equation:
cos(A) = 1 / (2 - 2sin^2(A) - 1)
cos(A) = 1 / (1 - 2sin^2(A))
Cross-multiplying:
cos(A)(1 - 2sin^2(A)) = 1
Distributing:
cos(A) - 2sin^2(A)cos(A) = 1
Factoring out common term:
cos(A)(1 - 2sin^2(A)) = 1
Dividing both sides by cos(A):
1 - 2sin^2(A) = 1 / cos(A)
Using the Pythagorean Identity:
1 - 2sin^2(A) = sec(A)
Substituting into the equation:
sec(A) = 1 / cos(A)
Using the Reciprocal Identity:
1 / cos(A) = sec(A)
Substituting sec(A) back into the equation:
1 - 2sin^2(A) = sec(A)
Adding 2sin^2(A) to both sides:
1 = sec(A) + 2sin^2(A)
Substituting the given equation:
1 = cos(A) * cos(2A) + 2sin^2(A)
Using the Identity:
cos(2A) = 2cos^2(A) - 1
Substituting into the equation:
1 = cos(A) * (2cos^2(A) - 1) + 2sin^2(A)
Expanding the equation:
1 = 2cos^3(A) - cos(A) + 2sin^2(A)
Simplifying the equation:
2cos^3(A) + 2sin^
The cosine double angle formula states that cos(2A) = 2cos^2(A) - 1.
Given:
cos(A) * cos(2A) = 1
Using the Cosine Double Angle Formula:
cos(2A) = 2cos^2(A) - 1
Substituting the given equation:
cos(A) * (2cos^2(A) - 1) = 1
Simplifying the equation:
2cos^3(A) - cos(A) = 1
Factoring out cos(A):
cos(A)(2cos^2(A) - 1) = 1
Dividing both sides by 2cos^2(A) - 1:
cos(A) = 1 / (2cos^2(A) - 1)
Using the Pythagorean Identity:
cos^2(A) + sin^2(A) = 1
Solving for sin^2(A):
sin^2(A) = 1 - cos^2(A)
Substituting into the equation:
cos(A) = 1 / (2(1 - sin^2(A)) - 1)
Simplifying the equation:
cos(A) = 1 / (2 - 2sin^2(A) - 1)
cos(A) = 1 / (1 - 2sin^2(A))
Cross-multiplying:
cos(A)(1 - 2sin^2(A)) = 1
Distributing:
cos(A) - 2sin^2(A)cos(A) = 1
Factoring out common term:
cos(A)(1 - 2sin^2(A)) = 1
Dividing both sides by cos(A):
1 - 2sin^2(A) = 1 / cos(A)
Using the Pythagorean Identity:
1 - 2sin^2(A) = sec(A)
Substituting into the equation:
sec(A) = 1 / cos(A)
Using the Reciprocal Identity:
1 / cos(A) = sec(A)
Substituting sec(A) back into the equation:
1 - 2sin^2(A) = sec(A)
Adding 2sin^2(A) to both sides:
1 = sec(A) + 2sin^2(A)
Substituting the given equation:
1 = cos(A) * cos(2A) + 2sin^2(A)
Using the Identity:
cos(2A) = 2cos^2(A) - 1
Substituting into the equation:
1 = cos(A) * (2cos^2(A) - 1) + 2sin^2(A)
Expanding the equation:
1 = 2cos^3(A) - cos(A) + 2sin^2(A)
Simplifying the equation:
2cos^3(A) + 2sin^
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
If cosA cos2A = 1 then the value of sin2A sin4A is?
Question Description
If cosA cos2A = 1 then the value of sin2A sin4A is? 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 cosA cos2A = 1 then the value of sin2A sin4A is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosA cos2A = 1 then the value of sin2A sin4A is?.
If cosA cos2A = 1 then the value of sin2A sin4A is? 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 cosA cos2A = 1 then the value of sin2A sin4A is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosA cos2A = 1 then the value of sin2A sin4A is?.
Solutions for If cosA cos2A = 1 then the value of sin2A sin4A is? 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 cosA cos2A = 1 then the value of sin2A sin4A is? defined & explained in the simplest way possible. Besides giving the explanation of
If cosA cos2A = 1 then the value of sin2A sin4A is?, a detailed solution for If cosA cos2A = 1 then the value of sin2A sin4A is? has been provided alongside types of If cosA cos2A = 1 then the value of sin2A sin4A is? theory, EduRev gives you an
ample number of questions to practice If cosA cos2A = 1 then the value of sin2A sin4A is? 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
|
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