Proof Of Trigonometric Identities?

Question

can you explain to me how to do this?
Sec s + Cot s Csc s = Csc^2 s Sec^2 s

Sorry the right equatio is
(Sec s + Cot s Csc s)/Cos s = Csc^2 s Sec^2 s

Answer 1

sec(s)+cot(s) cosec(s) =
= 1/cos(s) + cos(s)/sin(s) 1/sin(s) =
= 1/(sin^2(s) cos(s)) (sin^2(s) + cos^2(s))=
= 1/(sin^2(s) cos(s)) =
= cosec^2(s) sec(s)

which is slightly different from the formula given, but I believe it is the right identity.

Answer 2

Sec A + Cot A Csc A = Csc^2 A Sec^2 A
= Sec A + Cot A Csc A
= 1/ cos A + ( cos A/ sin A ) ( 1/ sin A)
= 1/ cos A + cos A / sin² A . .common denominator sin² A cos A
= ( sin² A + cos² A )/ (sin² A cos A)
= 1 / (sin² A cos A)
= csc² A sec A

Answer 3

Prove the identity.

[(sec s) + (cot s)(csc s)] / (cos s) = (csc²s)(sec²s)
____________

Left Hand Side = {(sec s) + (cot s)(csc s)} / (cos s)

= {1/(cos s) + [(cos s)/(sin s)] [1/(sin s)]} / (cos s)

= 1/(cos²s) + 1/(sin²s)

= (sec²s) + (csc²s)

= (sec²s)[(csc²s)(sin²s)] + (csc²s)[(sec²s)(cos²s)]

= [(sin²s) + (cos²s)] [(sec²s)(csc²s)]

= 1* [(sec²s)(csc²s)]

= [(sec²s)(csc²s)] = Right Hand Side

Answer 4

try writing it all in terms of sin and cosine.