Question

Question #78a09

Answer 1

Well, recall that:

• `tanx = sinx/cosx`
• `cotx = 1/tanx = cosx/sinx`
• `sin^2x + cos^2x = 1`
• `csc^2x = 1/sin^2x`

Thus:

`cot^2x(1+tan^2x)`

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

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

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

`= 1/sin^2x`

`= color(blue)(csc^2x)`