Question

(cotx + cscx(1-cosx)= SIN x

Answer 1

[AI-generated answer — Explain Bot]

To prove that cot(x) + csc(x)(1-cos(x)) = sin(x), we need to simplify the left side of the equation and show that it is equal to the right side.

Let's start by simplifying the left side:

cot(x) + csc(x)(1-cos(x))

Recall that cot(x) is equal to cos(x)/sin(x) and csc(x) is equal to 1/sin(x). Let's substitute these values in:

(cos(x)/sin(x)) + (1/sin(x))(1-cos(x))

Now, let's simplify the expression further:

(cos(x) + (1-cos(x)))/(sin(x))

Using the distributive property, we can simplify the numerator:

(1)/(sin(x))

The equation becomes:

1/sin(x) = sin(x)

Now, let's simplify the right side of the equation:

sin(x)

Since 1/sin(x) is equal to csc(x), the equation becomes:

csc(x) = sin(x)

Therefore, we have proved that cot(x) + csc(x)(1-cos(x)) is equal to sin(x).