Question

Prove that....::(Cosecx-Sinx) (Secx-Cosx) (Cotx-Tanx)=1

Answer 1

here there is a mistake in your problem cotx +tanx it is not cotx-tanx
lhs = (cosec x -sin x) (sec x-cos x) (cot x+tanx)

= sinx (cosecx-sinx) cosx(secx-cosx)(cotx+tanx)/sinxcosx
=[sinxcosecx-sin²x][cosxsecx-cos²x](cotx +tanx)/sinxcosx
=(1-sin²x) (1-cos²x)(cotx +tanx)/sinxcosx
=[cos²xsin²x(cosx/sinx +sinx/cosx]/sinxcosx
=cos²xsin²x (cos²x+sin²x)/sin²xcos²x
=cos²x+sin²x
=1
rhs

Answer 2

Answer:

Step-by-step explanation:

Your question is wrong if we try(cosecx-sinx)(secx-cosx)(cotx-tanx)=1 then we will get the following result shown in 2nd picture.