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Question

Show that sinθ = cosθ tanθ

Answer 1

Start with the right hand side:

(cos θ)(tan θ)

Change tangent to the ratio of sine to cosine.

cosθ [(sin θ) /(cos θ)]

The cosine divides out

sin θ

which is the left hand side!

Answer 2

sinθ = cosθ tanθ

sinθ = cosθ (sinθ/cosθ)

cosθ cancels.

sinθ = sinθ

Answer 3

Let ABC be a triangle with a right-angle at B.

Then from the deifinitions of the ratios:
sin(A) = CB / AC
cos(A) = AB / AC
tan(A) = CB / AB

cos(A)tan(A)
= (AB/AC) * (CB/AB)
= CB / AC
= sin(A).