sin x + cot x cos x = csc x Use the fundamental identities to verify the following identities.?

Question

Show all of your work, including what calculator steps you used, if any

Answer 1

sin x + cot x cos x = csc xs5n x*

sin x + (cos x)(cos x)/(sin x) = csc x

sin x + (cos² x)/(sin x) = csc x

(sin² x + cos² x)/sin x = csc x

but sin² x + cos² x = 1

therefore:

1/(sin x) = csc x

csc x = csc x

Proven!

Answer 2

sin x + cos x cot x = csc x replace cot by potential of cos x / sin x sin x + cos x (cos x / sin x) = csc x exhibit as a single fraction liquid crystal reveal =Sin x (sin^2 x + cos^2 x)/sin x = csc x pythagorean relation: sin^2 x + cos^2 x = a million a million/sin x = csc x inverse relation (reciprocal) a million/sin x = csx x csc x = csc x

Answer 3

Prove the identity.

sin x + cot x cos x = csc x

Let's start with the left hand side.

Left Hand Side = sin x + cot x cos x

= sin²x/sin x + (cos x/sin x) cos x = sin²x/sin x + cos²x/sin x

= (sin²x + cos²x)/sin x = 1/sin x = csc x = Right Hand Side

Answer 4

L.H.S. sinx + cotx cosx
= sinx + (cosx / sinx )cosx As cotx = cosx / sinx
= sin x + cos^2 x / sinx
=(sin^2x +cos^2 x) / sin x Taking L.C. M. sinx
= 1/sinx By sin^2x +cos^2 x =1
= csc x
= R.H.S.

Hence, sin x + cot x cos x = csc x , Proved