samigupta8
  • samigupta8
eliminate θ between cosecθ-sinθ=m and secθ-cosθ=n
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ash2326
  • ash2326
\[cosec\ \theta -\sin \theta=m\] @samigupta8 Please tell me what's the relation between sin and cosec?
samigupta8
  • samigupta8
don't u know it
ash2326
  • ash2326
I do know, but I'm asking you so that you also take part in the process of answering

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More answers

samigupta8
  • samigupta8
cotθcosθ=m
ash2326
  • ash2326
Let me rephrase, how cosec x and sin x are related?
samigupta8
  • samigupta8
yes
samigupta8
  • samigupta8
1/sinθ-sinθ=m
ash2326
  • ash2326
yes, so we'll get \[\frac{1-\sin^2 \theta}{\sin \theta}=m\] or \[\frac{\cos^2 \theta}{\sin \theta} =m\] or \[\cot \theta \cos \theta =m\]Can you simplify the second equation?
ash2326
  • ash2326
\[\sec \theta -\cos \theta =n\]
samigupta8
  • samigupta8
sinθtanθ=n
samigupta8
  • samigupta8
then next
ash2326
  • ash2326
Yes, I'm thinking
samigupta8
  • samigupta8
kk.....
ash2326
  • ash2326
OK, let's multiply these two, we'd get \[\sin \theta \cos \theta= mn\] Now we'll square and add the two equations \[(cosec \theta -\sin \theta)^2+(\sec \theta -\cos \theta)^2=m^2+n^2\] \[cosec^2 \ \theta +\sin^2 \theta-1+\sec^2 \theta +\cos^2 \theta -1=m^2+n^2\] \[cosec^2 \ \theta+\sec^2 \theta +1-1-1=m^2+n^2\] Do you understand this?
samigupta8
  • samigupta8
ya...
ash2326
  • ash2326
Next we'll write cosec in terms of sin and sec in terms of cos. Can you try? \[\cos \theta\sin \theta =mn\]
samigupta8
  • samigupta8
i m getting it as 1-m^2 n^2=(m^2-n^2)m^2 n^2
ash2326
  • ash2326
Check again, I got \[(m^2+n^2+1)(mn)^2=1\]
samigupta8
  • samigupta8
i got it as (mn)^2+(mn)^2(m^2+n^2=1
samigupta8
  • samigupta8
yeasss... u are ryt
ash2326
  • ash2326
Interim steps are \[\frac{1}{\sin^2 x}+\frac{1}{\cos^2 x}-1=m^2+n^2\] \[\frac{\cos^2 x+\sin^2 x}{\cos^2 x \times \sin^2 x}-1=m^2+n^2\] \[\frac{1}{(mn)^2}-1=m^2+n^2\]
samigupta8
  • samigupta8
btt answer is given as(m^2n)^2/3+(mn^2)^2/3=1
samigupta8
  • samigupta8
how is this ans coming

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