Question

`cos(A)/(1-sin(A))=(1+sin(A))/cos(A)`??

Answer 1

Prove: `cos(A)/(1-sin(A))=(1+sin(A))/cos(A)`

Multiply the left side by 1 in the form of `cos(A)/cos(A)`:

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

Substitute `cos^2(A) = 1-sin^2(A)`

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

Factor the numerator:

`((1-sin(A))(1+sin(A)))/(cos(A)(1-sin(A)))=(1+sin(A))/cos(A)`

Cancel the common factor:

#(cancel((1-sin(A)))(1+sin(A)))/(cos(A)cancel((1-sin(A))))= (1+sin(A))/cos(A)#

Write without the cancelled factors:

#(1+sin(A))/cos(A)= (1+sin(A))/cos(A)# Q.E.D.