Question

prove that sin a/1-cos a =cosec a+ cot a​

Answer 1

Answer:

GIVEN LHS is sin a /1-cos a  

multiply and divide by 1-cos a

we get

sin a (1-cos a)/                                 (numerator)

(1+cos a)(1-cos a)                             (denominator)              

use the formula (A+B)(A-B)=A^2-B^2

we get

sin A(1-cosA)/

1-cos^2 A

using formula Sin^2 A+cos^2 A=1

we get Sin^2 A= 1-cos^2A

substituting

we get

SinA(1-cos A)/

sin^2 A

we get

1-cos A/

sin A

=  1/                    -cos A/

  sinA                 sin A

=   cosec A -cot A

so actually i think in the question it must be (- cotA)

thank you    

Answer 2

Answer:

L. H. S

sina/1-cosa

=sina*(1+cosa)/((1-cosa) *(1+cosa)

=sina*(1+cosa)/(1-cosa^2)

=sina*(1+cosa)/((sina) ^2)

=(1+cosa)/(sina)

R. H. S

coseca+cota

=1/(sina) +cosa/(sina)

=1+cosa/(sina)

L. H. S=R.H.S

hence proved