Question

Question #0c317

Answer 1

`1/ (sin(x)cos(x))`

Explanation:

Remember the trigonometric identities

• `sin^2(x) + cos^2(x) = 1`
• `tan^2(x) + 1 = sec^2(x)`
• `cot^2(x) + 1 = csc^2(x)`

So

`cot(x)sec^2(x)`

`=cot(x)[tan^2(x) + 1]`

`=tan(x) + cot(x)`

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

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

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

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