93
Question
Eliminate ′θ′ from tanθ+sinθ=m,tanθ−sinθ=n.
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Solution
tanθ+sinθ=msinθcosθ+sinθ=msinθ(1+cosθcosθ)=m→1tanθ−sinθ=nsinθ(1−cosθcosθ)=n→2Dividing the equations 121+cosθcosθ1−cosθcosθ=mn1+cosθ1−cosθ=mnn+ncosθ=m−mcosθ(m+ncosθ)=m−ncosθ=m−nm+nθ=cos−1(m−nm+n)Equations are
tan(cos−1(m−nm+n))+sin(cos−1(m−nm+n))=mtan(cos−1(m−nm+n))−sin(cos−1(m−nm+n))=m
tanθ+sinθ=m
sinθcosθ+sinθ=m
sinθ(1+cosθcosθ)=m→1
tanθ−sinθ=n
sinθ(1−cosθcosθ)=n→2
Dividing the equations 12
1+cosθcosθ1−cosθcosθ=mn
1+cosθ1−cosθ=mn
n+ncosθ=m−mcosθ
(m+ncosθ)=m−n
cosθ=m−nm+n
θ=cos−1(m−nm+n)
Equations are
tan(cos−1(m−nm+n))+sin(cos−1(m−nm+n))=m
tan(cos−1(m−nm+n))−sin(cos−1(m−nm+n))=m
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