If tanθ+sinθ=m and tanθ-sinθ=n,then show that m^2-n^2=4√mn CLASS-10 TRIGONOMETRY IMPORTANT PROBLEM

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If tanθ+sinθ=m and tanθ-sinθ=n,then show that m^2-n^2=4√mn
  1. KHAJA ACADEMY MATHEMATICA
  2. #If tanθ sinθ=m and tanθ-sinθ=n
  3. #m square - n square
  4. #4root mn
  5. #class 10 trigonometry important problem
  6. #10th class cbse maths trigonometry
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Комментарии
Автор

Understood sir.
Thank you for simplifying the tough problem in a easy way

selinasharma
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Superb explanation👌
🎩
😁
👕👍Great!
👖

dasguptad
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VERY WELL EXPLAINED
VERY HELPFUL THANK YOU

harivilluhotelsmadanapally
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Thank you sirr you make this so simple ❤ I'll never forget this

arshilsiddique
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Sir, this can be done in another way.
Given, tan theta + sin theta = m ___(i)
tan theta - sin theta = n ___ (ii)
Adding (i) and (ii)
tan theta + sin theta + tan theta - sin theta = m + n
2tan theta = m + n
tan theta = (m + n)/2
therefore, cot theta = 2/(m + n)
Similarly if we subtract (i) from (ii) we will get,
sin theta = (m - n)/2
Therefore, cosec theta=2/(m-n)
We know,
cosec²theta - cot²theta = 1
So,
{2/(m - n)}² - {2/(m + n)}² = 1
=> 4/(m - n)² - 4/(m + n)² = 1
Taking 4 as common,
=>4{1/(m - n)² - 1/(m + n)²} = 1
=>4[ {(m + n)² - (m - n)²}/(m - n)² (m + n)²] = 1
After simplifying this expression we will get,
=> 4{ 4mn /(m² - n²)²} = 1
=> 16mn/(m² - n²)² = 1
=> 16mn = (m² - n²)²
=>(m² - n²) = +-√16mn
=>m² - n² = +-4√mn
So, one of the solutions of the equation is m² - n² = 4√mn
So, L.H.S = R.H.S
Hence, proved.

Aspirant-yygm
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Thank you sir.
I appreciate your help

soundaryakrishna
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Thankyou sir my dout is crystal clear ❤❤

rupeshlovewanshi
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You are a great teacher. , i am really grateful to you 🙏

boreduser
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Sir, what if we need to find the vlue of n where others are given please let me know.

gamingwithzinan
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This question seems like it's tough but in real it isn't:)) btw thankyusm for easy explanation ❤️‍🔥

asmrbooo
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Mai hindi medium se hu but l like this method 👌

AnamikaPrajapati