Question

How to prove

Pls answer

Answer 1

Answer:

I HAVE PROVED THE GIVEN EQUATION BELOW.

HOPE IT HELPS.

Step-by-step explanation:

Given that,

    sqrt(  1-cosΘ / 1+cosΘ )= cosecΘ - cotΘ

LHS : = sqrt(  1-cosΘ / 1+cosΘ )

           we know that,

                     1-cosΘ = 2sin²Θ/2

                     1+cosΘ = 2cos²Θ/2

applying that,

   =   sqrt( 2sin²Θ/2 / 2cos²Θ/2)

    = sqrt ( sin²Θ/2 / cos²Θ/2)

    = sinΘ/2 / cosΘ/2

   = tanΘ/2 --------------(1)

RHS: = cosecΘ - cotΘ

        = 1/ sinΘ  - cosΘ / sinΘ

        = 1-cosΘ / sinΘ

       = 2sin²Θ/2 / sinΘ

      = 2 sin²Θ/2 / 2 sinΘ/2 cosΘ/2

      =sinΘ/2 / cosΘ/2

       = tanΘ/2 --------------(2)

                      therefore, (1) = (2)

                                  LHS  = RHS

                          sqrt(  1-cosΘ / 1+cosΘ )= cosecΘ - cotΘ

                                    HENCE PROVED.