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:

AllAboutCircuits

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.