Question

sinx/1+cosx + 1+cosx/sinx = 2cscx prove that this equation is an identity.

Answer 1

1st u gotta get like denominators so multiply both sides by the denominator of the opposite side u will end up with sinx^2/sinx(1+cosx).. + ..1+2cosx+cosx^2/sinx(1+cosx)
next add ....sinx^2 (from the numerator of the 1st fraction) + cosx^2(from the numerator of the 2nd fraction) =1 so the combined new fraction is 1+1+2cosx/sinx(1+cosx) which = 2+2cosx/sinx(1+cosx) now factor the numerator 2(1+cosx)/sinx(1+cosx) then u can cancel the cosx from the numerator and the denominator and u r left with 2/sinx where 1/sinx=cscx which is a reciprocal identity so 2/sinx =2cscx .... hope u understand all that