Question

1 + cosec A / cosec A = cos²A / 1-sin A​

Answer 1

Answer:

proof:

Step-by-step explanation:

cosec A=1/sin A

hence,L.H.S= (1+1/sinA)sinA=sinA +1

                         =(1+sinA)(1-sinA)/(1-sinA)......(multiply and dividing by1-sinA)

                                  =(1-sin²A)/(1-sinA)...........................(a+b)(a-b)=a²-b²

                                 =cos²A/(1-sinA)

                                 =R.H.S

Answer 2

Answer:

proved LHS=RHS

Step-by-step explanation:

cos^2(A)/(1-sinA)=LHS

=cos^2(A)*(1+sinA)/(1-sinA)*(1+sinA)

{divide and multiply with 1+sinA}

=cos^2(A)*(1+sinA)/(1-sin^2(A))

{(a-b)*(a+b)=a^2-b^2}

=cos^2(A)*(1+sinA)/(cos^2(A))

{1-sin^2(A)=cos^2(A)}

=1+sinA

=1+(1/cosecA)

{sinA =1/cosecA}

Taking LCM

=1+cosecA/cosecA

=RHS