Defence Exam > Defence Questions > If sinθ = (m2– n2)/(m2+ n2) and 0...
Start Learning for Free
If sinθ = (m2 – n2)/(m2 + n2) and 0 < θ < π/2, then what is the value of cosθ?
- a)2mn/(m2 + n2)
- b)2mn/(m2 - n2)
- c)(m2 + n2)/2mn
- d)(m2 - n2)/2mn
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2...
sinθ = (m2 – n2)/(m2 + n2)
Squaring on both the sides
Squaring on both the sides
Sin2θ = (m2 – n2)2/(m2 + n2)2 [∵ (a – b)2 = (a + b)2 – 4ab]
Sin2θ = [(m2 + n2)2 – 4m2n2]/(m2 + n2)2 [∵ (a – b)2 = (a + b)2 – 4ab]
Sin2θ = 1 – 4m2n2/(m2 + n2)2
4m2n2/(m2 + n2)2 = 1 – sin2θ
4m2n2/(m2 + n2)2 = 1 – sin2θ
4m2n2/(m2 + n2)2 = cos2θ [∵ sin2θ + cos2θ = 1]
Taking the square roots
∴ 2mn/(m2 + n2) = cosθ
Taking the square roots
∴ 2mn/(m2 + n2) = cosθ
Most Upvoted Answer
If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2...
Given Information:
- sinθ = (m2– n2)/(m2+ n2)
- 0 < θ="" />< />
To Find:
Value of cosθ
Solution:
Step 1: Use the trigonometric identity sin^2θ + cos^2θ = 1
Step 2: Substitute sinθ from the given information
(sinθ)^2 + cos^2θ = 1
[(m2– n2)/(m2+ n2)]^2 + cos^2θ = 1
(m2– n2)^2/(m2+ n2)^2 + cos^2θ = 1
Step 3: Simplify the equation
(m2 - n2)^2 + cos^2θ * (m2 + n2)^2 = (m2 + n2)^2
(m2 - n2)^2 + cos^2θ * (m2 + n2)^2 = m2^2 + 2mn + n2^2
Step 4: Solve for cos^2θ
cos^2θ = (m2^2 + 2mn + n2^2 - (m2 - n2)^2)/(m2 + n2)^2
cos^2θ = (4m^2n^2)/(m2 + n2)^2
cosθ = 2mn/(m2 + n2) (Taking square root on both sides)
Therefore, the value of cosθ is option A) 2mn/(m2 + n2).
- sinθ = (m2– n2)/(m2+ n2)
- 0 < θ="" />< />
To Find:
Value of cosθ
Solution:
Step 1: Use the trigonometric identity sin^2θ + cos^2θ = 1
Step 2: Substitute sinθ from the given information
(sinθ)^2 + cos^2θ = 1
[(m2– n2)/(m2+ n2)]^2 + cos^2θ = 1
(m2– n2)^2/(m2+ n2)^2 + cos^2θ = 1
Step 3: Simplify the equation
(m2 - n2)^2 + cos^2θ * (m2 + n2)^2 = (m2 + n2)^2
(m2 - n2)^2 + cos^2θ * (m2 + n2)^2 = m2^2 + 2mn + n2^2
Step 4: Solve for cos^2θ
cos^2θ = (m2^2 + 2mn + n2^2 - (m2 - n2)^2)/(m2 + n2)^2
cos^2θ = (4m^2n^2)/(m2 + n2)^2
cosθ = 2mn/(m2 + n2) (Taking square root on both sides)
Therefore, the value of cosθ is option A) 2mn/(m2 + n2).
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer?
Question Description
If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer?.
If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If sinθ = (m2– n2)/(m2+ n2) and 0 < θ < π/2, then what is the value of cosθ?a)2mn/(m2+ n2)b)2mn/(m2- n2)c)(m2+ n2)/2mnd)(m2- n2)/2mnCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence 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