Question

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

Answer 1

Let's see

`\\ \rm\Rrightarrow (sin^2x+cos^x)/(sinx)`

• sin²x+cos²x=1

`\\ \rm\Rrightarrow (1)/(sinx)`

`\\ \rm\Rrightarrow cosecx`

Answer 2

cosec x

(or csc x)

Explanation:

Trig Identities

`\sf \sin^2 x + \cos^2 x=1`

`\sf (1)/(\sin x)=cosec\: x`

Therefore,

`\begin{aligned}\implies \sf (\sin^2x + \cos^2x)/(\sin x) &= \sf(1)/(\sin x)\\\\ & = \sf cosec\:x \end{aligned}`