JEE Exam > JEE Questions > Find range of sin2x + sinx + cosx?
Start Learning for Free
Find range of sin2x + sinx + cosx?
Most Upvoted Answer
Find range of sin2x + sinx + cosx?
Range of sin2x sinx cosx
Let's first break down the expression sin2x sinx cosx:
- sin2x = 2sinx cosx (using the double angle identity)
- sin2x sinx cosx = 2sinx cosx * sinx cosx = 2sin^2x cos^2x
Now, we can rewrite the expression as:
- 2sin^2x cos^2x = sin^2x (2cos^2x) = cos^2x (2sin^2x)
Since both sin^2x and cos^2x are always between 0 and 1, we know that:
- 2sin^2x cos^2x is always between 0 and 1
- sin^2x (2cos^2x) is always between 0 and 1
- cos^2x (2sin^2x) is always between 0 and 1
Therefore, the range of sin2x sinx cosx is:
- 0 ≤ sin2x sinx cosx ≤ 1
This means that the expression can take any value between 0 and 1, inclusive.
Community Answer
Find range of sin2x + sinx + cosx?
Sinx + cosx = 2sinxcosx
also sin2x= 2sinx cox
adding both we get 4sinxcosx
which is equal to 2sin2x
range = [-2,2]
also sin2x= 2sinx cox
adding both we get 4sinxcosx
which is equal to 2sin2x
range = [-2,2]
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Find range of sin2x + sinx + cosx?
Question Description
Find range of sin2x + sinx + cosx? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find range of sin2x + sinx + cosx? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find range of sin2x + sinx + cosx?.
Find range of sin2x + sinx + cosx? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find range of sin2x + sinx + cosx? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find range of sin2x + sinx + cosx?.
Solutions for Find range of sin2x + sinx + cosx? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Find range of sin2x + sinx + cosx? defined & explained in the simplest way possible. Besides giving the explanation of
Find range of sin2x + sinx + cosx?, a detailed solution for Find range of sin2x + sinx + cosx? has been provided alongside types of Find range of sin2x + sinx + cosx? theory, EduRev gives you an
ample number of questions to practice Find range of sin2x + sinx + cosx? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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