Prove the following identities (1-16)cosec x (sec x-1)-cot x (1-cos x)=tan x-sin x plixxxnmdjdkj

Welcome to askiitians

LHS=cosecx(secx−1)−cotx(1−cosx)
=1/sinx(1/cosx−1)−cosx/sinx(1−cosx)
=1/sinx(1−cosx/(cosx) )−cosx/sinx(1−cosx)
=(1−cosx/sinx)(1/cosx−cosx)=(1−cosx)/(sinx)(1−cos2x/cosx)
=(1−cosx/sinx)(sin2x/cosx)
=(1−cosx)(sinx/cosx)
=sinx/cosx−sinx=tanx−sinx
=RHS
Henceproved
Thanks