Menu Close

prove-cosec-2-cot-cosec-1-




Question Number 47836 by Aknabob1 last updated on 15/Nov/18
prove cosec^2 θ−cotθcosecθ=1
provecosec2θcotθcosecθ=1
Answered by $@ty@m last updated on 15/Nov/18
LHS=cosec^2 θ−cotθcosecθ  =cosec^2 θ−((cos θ)/(sin θ))×(1/(sin θ))  =(1/(sin^2 θ))−((cos θ)/(sin^2 θ))  =((1−cos θ)/(sin^2 θ))  =((1−cos θ)/(1−cos^2 θ))  =(1/(1+cos θ))  ≠1  The question is wrong.  May be typo error.  Pl. check
LHS=cosec2θcotθcosecθ=cosec2θcosθsinθ×1sinθ=1sin2θcosθsin2θ=1cosθsin2θ=1cosθ1cos2θ=11+cosθ1Thequestioniswrong.Maybetypoerror.Pl.check
Commented by Aknabob1 last updated on 15/Nov/18
thanks i appreciate
thanksiappreciate
Answered by peter frank last updated on 15/Nov/18
cosecθ(cosecθ−cotθ)  cosecθ((1/(sinθ))−((cosθ)/(sinθ)))  ((cosecθ)/(sinθ))(1−cosθ)  ((1−cosθ)/(sin^2 θ))=((1−cosθ)/(1−cos^2 θ))                =((1−cosθ)/(1+cosθ))  hence  cosec^2 θ−cotθcosecθ≠1
cosecθ(cosecθcotθ)cosecθ(1sinθcosθsinθ)cosecθsinθ(1cosθ)1cosθsin2θ=1cosθ1cos2θ=1cosθ1+cosθhencecosec2θcotθcosecθ1
Commented by Aknabob1 last updated on 15/Nov/18
thanks i appreciate
thanksiappreciate

Leave a Reply

Your email address will not be published. Required fields are marked *