sin x + cos x

-------------- = ?
sin x

sin x cos x
----- + ----- =
sin x sin x

cos x/sin x = cot x

this is what i got, the problem is we have a match the expression to the equation work sheet and this is not one of the answers. need to figure out what im doing wrong so i can get the rest worked right. thanks

I do not see why you changed the + into a ÷, namely:

from:
sin x cos x
----- + ----- =
sin x sin x
(which I see as sin/sin+cos/sin)

But sin x/sin x = 1, and
cos x/sin x = cot x
so the sum is 1 + cot x.

not quite, but you are close

(sinx + cosx)/sinx
= sinx/sinx + cosx/sinx
= 1 + cotx

you left out the "1"

To determine what you might have done wrong, let's go through the steps of simplifying the expression again:

Starting with the expression: (sin x + cos x) / sin x.

Step 1: Distribute the sin x denominator to both terms in the numerator:
sin x / sin x + cos x / sin x.

Step 2: Simplify the fractions:
1 + cos x / sin x.

Step 3: Recognize that 1 is equivalent to sin x / sin x:
sin x / sin x + cos x / sin x.

Step 4: Combine the two fractions:
(sin x + cos x) / sin x.

From the given equation, cos x / sin x = cot x. This equation states that the ratio of the cosine of an angle to the sine of that angle is equal to the cotangent of that angle. However, in this case, we do not have the ratio of cosine to sine directly.

So, based on this analysis, it seems that the answer you derived (cos x / sin x = cot x) is not relevant to the original expression (sin x + cos x) / sin x. Therefore, it is likely that you made an error during the simplification of the expression. Please review the steps provided above and ensure correct execution.