Question

Verify this problem please? 1 + cosx/sinx = csc x + cotx

Answer 1

Let us, do the right-hand-side

$\bf csc(x)+cot(x)\qquad \begin{cases} cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)} \\\\ % cosecant csc(\theta)=\cfrac{1}{sin(\theta)} \end{cases}\qquad thus \\\\\\ \cfrac{1}{sin(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{1+cos(x)}{sin(x)} \\\\\\ thus\implies 1+\cfrac{cos(x)}{sin(x)}\ne csc(x)+cot(x)$

Answer 2

=1/sin x + cos x/sin x
= csc x + cot x