Question

How do you verify `sinx + cosx cotx = cscx`?

Answer 1

Left Hand Side :

`sinx + cosx cotx`

We know that `color(blue)(cot x = cos x / sin x`

Therefore `sinx + cosx cotx = sin x + cos x* (cos x/ sinx)`

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

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

(We know the Trigonometric Identity
`color(blue)( sin^2x + cos ^ 2 x = 1`)

`= 1 / sinx`

`= csc x` (Because Cosecant is the reciprocal of Sine)

Hence Proved.