Question

Simplify the expression.
(1 - cot x) / tan x - 1

Answer 1

substitute the value of cot x and tan x i hope u will get the ans

Answer 2

What?

Answer 3

well, keeping in mind that cot= cos/sin, and tan = sin/cos
let's use that atop and below
$$
\cfrac{1-cot(\theta)}{tan(\theta)-1}
\implies
\cfrac{
1-\frac{cos(\theta)}{sin(\theta)}
}
{
\frac{sin(\theta)}{cos(\theta)}
}
$$

Answer 4

hemm I missed something :/

Answer 5

-2

Answer 6

$$
\cfrac{1-cot(\theta)}{tan(\theta)-1}
\implies
\cfrac{
1-\frac{cos(\theta)}{sin(\theta)}
}
{
\frac{sin(\theta)}{cos(\theta)}-1
}
$$

Answer 7

so, there, add both, atop and bottom, what do you get?

Answer 8

Add what?

Answer 9

the fractions :/

Answer 10

How?

Answer 11

$$
\cfrac{1-cot(\theta)}{tan(\theta)-1}
\implies
\cfrac{
1-\frac{cos(\theta)}{sin(\theta)}
}
{
\frac{sin(\theta)}{cos(\theta)}-1
}
\implies
\large {
\color{red}{
\cfrac{
\frac{1}{1}-\frac{cos(\theta)}{sin(\theta)}
}
{
\frac{sin(\theta)}{cos(\theta)}-\frac{1}{1}
}}
}
$$

Answer 12

let's try first the numerator

Answer 13

(1 - cos(x))/1 - sin(X) ?

Answer 14

\(\frac{1}{1}-\frac{cos(\theta)}{sin(\theta)}\) what would be your LCD there?

Answer 15

sin (x)

Answer 16

right, so let's use that, to get
$$
\frac{1}{1}-\frac{cos(\theta)}{sin(\theta)}
\implies \frac{sin(\theta)-cos(\theta)}{sin(\theta)}
$$

Answer 17

Ok. then the denominator would just be cos (x) - sin (x) / cos (x)

Answer 18

right

Answer 19

well, one sec

Answer 20

the denominator will be sin-cos/cos

Answer 21

right. sorry.

Answer 22

so sin-cos/sin / (sin-cos/cos)?

Answer 23

$$\large {
\cfrac{
\frac{sin(\theta)-cos(\theta)}{sin(\theta)}
}{
\frac{sin(\theta)-cos(\theta)}{cos(\theta)}
}
\implies
\frac{sin(\theta)-cos(\theta)}{sin(\theta)} \times
\frac{cos(\theta)}{sin(\theta)-cos(\theta)}
}
$$

Answer 24

so, there are 2 guys to cancel out, and you're left with just a function :)

Answer 25

cot x

Answer 26

Ok. Thank you!! :)

Answer 27

yw