Question

1_cos theta/sin theta=sin theta/1+cos theta

Answer 1

LHS=

1-cosФ/sinФ

    * Multiplying numerator and denominator with sinФ, we get

sinФ-cosФ×sinФ / sinsquareФ

              *Taking sinФ common from numerator, we get

sinФ × ( 1- cosФ ) / sin squareФ

                  *sin squareФ = 1- cos square Ф-----by applying this

sinФ × (1-cosФ) / 1- cos squareФ

            *denominator  =       1 - cos squareФ = 1 square - cos squareФ

                                         = (1+cosФ)(1-cosФ)

 sinФ(1-cosФ) / (1+coФ)(1-cosФ)

                * (1-cosФ ) will get cancelled in numerator and denominator

Hence we get sinФ/1+cosФ ---hence proved !

 

Answer 2

It is given that

1-cos a/sin a = sina /1+cos a

prove :-

let Lhs be 1-cos a /sina

= Now crossing ,we get

(1+cos a)(1-cos a)=sin2a

now applying identity we get

$1 - {cos}^{2} = {sin}^{2}$

now,that

${sin}^{2} = {sin}^{2}$