Trigonometric Equation

[Sabellic]

1. The problem statement, all variables and given/known data
If cos x = a/b and tan x = c/d; where a, b, c do not equal 0, then sin x is.....

(a) bd/ac
(b) bc/ad
(c) ad/bc
(d) ad/bc


2. Relevant equations
http://www.bymath.com/studyguide/tri/sec/tri5a.gif
http://www.mathacademy.com/pr/prime/articles/trig_ident/trig_ident_6.gif


3. The attempt at a solution

The way I see it, if cos x = a/b, then b=hypotenuse.
if tan x = c/d, then d= hypotenuse (two hypotenuse values?) and c = opposite.

Therefore sin x = c/d. I don't know why the answers in the book use products of the vairables in their numerators and denominators.

Please help.

Much thanks in advance.

[happyg1]

Hmmm... Your c) and d) choices are the same..and the tan doesn't involve the hypotenuse.
Are you sure you copied the whole thing right?

[HallsofIvy]

Since
tan \alpha= \frac{sin \alpha}{cos \alpha}
multiplying on both sides by cos(\alpha) gives

sin(\alpha)= cos(\alpha)tan(\alpha)
That's all you need.