Question

Question #781b9

Answer 1

We will use the following:

• `cot(x) = cos(x)/sin(x)`
• `csc(x) = 1/sin(x)`
• `sin^2(x)+cos^2(x) = 1`
  `=> cos^2(x) = 1-sin^2(x)`
• `a^2-b^2 = (a+b)(a-b)`

`cot^2(x)/(1+csc(x)) = (cos(x)/sin(x))^2/(1+1/sin(x))`

`=(cos^2(x)/sin^2(x))/(1+1/sin(x))`

`=cos^2(x)/(sin^2(x)+sin(x))`

`=(1-sin^2(x))/(sin(x)(1+sin(x)))`

`=((1+sin(x))(1-sin(x)))/(sin(x)(1+sin(x)))`

`=(1-sin(x))/sin(x)`