Question

Verify the following trigonometric identity: (csc x + cot x)^2 = cos x +1/ 1- cos x

Answer 1

9514 1404 393

Step-by-step explanation:

As written, the equation is not an identity. Perhaps you want to show ...

(csc(x) +cot(x))² = (cos(x) +1)/(1 -cos(x))

__

We will transform the left-side expression to the form of the right-side expression.

`(\csc(x)+\cot(x))^2=\left((1)/(\sin(x))+(\cos(x))/(\sin(x))\right)^2=((1+\cos(x))^2)/(\sin(x)^2)\\\\=((1+\cos(x))^2)/(1-\cos(x)^2)=(1+\cos(x))/(1-\cos(x))\cdot(1+\cos(x))/(1+\cos(x))=\boxed{(\cos(x)+1)/(1-\cos(x))}`