Question

prove that (cosec theta - sin teta)(sec tetta -cos tetta)(tan teta -cot teta) = 1

Answer 1

Let theta be x for my ease..
Convert everything in sin and cos
After converting we shall get
=(1/sinx-sinx)(1/cosx-cosx)(sinx/cosx-cosx/sinx)
=(1-sin sq.x/sinx)(1-cos sq. x/cosx)
(sin sq. x-cos sq. x / sinxcosx)
=(cos sq. x/ sinx)(sin sq. x/cosx)
(sin sq. x-cos sq. x / sinxcosx)
=sinx cosx(sin sq. x-cos sq. x / sinxcosx)
=sin sq. x - cos sq. x [ANSWER]
ALTHOUGH IT SHOULD BE (TAN THETA + COT THETA) IN THE QUESTION TO GET ANSWER = 1