verify the identity cot x/sec x = csc x - sin x

Question

please answer.

Answer 1

kotan/sekant=(kosine/sine) /(sekant)...kosine*kosine/sine

csc=(1/sine), so abuv stuf=kosine^2*csc

kosine^2=(1-sine^2), so yu hav (1-sine^2)/sine...(1/sine) -(sine^2/sine)

=csc-sine

Answer 2

cot x/sec x = csc x - sin x

From RHS cotx/secx

=cotxcosx

=[cosx/sinx]cosx

=cos^2(x)/sinx

=[1-sin^2(x)]/sinx

=[1/sinx]-[sin^2(x)/sinx]

=cscx-sinx Verified

Therefore, it is an identity