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

3 Answers

LHS=>sinx/cscx

=> sinx*1/cscx

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

"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

See Below.

Explanation:

AllAboutCircuitsAllAboutCircuits

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.