Question

How do you verify the identify `sintheta/csctheta=sin^2theta`?

Answer 1

`LHS=>sinx/cscx`

`=> sinx*1/cscx`

`=>sinx*sinx = sin^2 x` since, `sinx=1/cscx`

Answer 2

`"please look at the following explanation."`

Explanation:

`csc=1/sin theta`

`"write "1/sin theta " instead " csc theta " in the equation " sin theta/ csc theta`

`sin theta/(1/sin theta)=sin theta*sin theta/1=sin^2 theta`

Answer 3

See Below.

Explanation:

Trigonometric Ratios are of 6 kinds.

`sin x = "opposite"/"hypotenuse" = "perpendicular"/"hypotenuse"`

`cos x = "adjacent"/"hypotenuse" = "base"/"hypotenuse"`

`tan x = "opposite"/"adjacent" = "perpendicular"/"base"`

`csc x = "hypotenuse"/"opposite" = "hypotenuse"/"perpendicular"`

`sec x = "hypotenuse"/"adjacent" = "hypotenuse"/"base"`

`cot x = "adjacent"/"opposite" = "base"/"perpendicular"`

So, you can see that, `csc x` is the inverse of `sin x`.

So,

L.H.S = `sin x/csc x = sin x * 1/csc x = sin x * sin x = sin^2 x` = R.H.S

Hence Proved.