simplify sinx cotx

Question

I have an exam soon, our maths teacher is hopeless and dad is too impatient. Can anyone please tell me how to work this out? Thanks.

Answer 1

sinx cotx=sinx * (cosx/sinx)=cosx

Answer 2

For a right-angled triangle sin(x)=O/H [where O is the side opposite the angle x and H is the hypotenuse] while cot(x)=A/O [where A is the side adjecent to x and H is again the hypotenuse.

Therefore sin(x)cot(x)=O/H*A/O=OA/HO=A/H. Cos(x)=A/H. So sin(x)cot(x)=cos(x).