Question

integration of 1 + cos x/1 - cos x dx​

Answer 1

Answer:

(1+cos x)/(1-cos x)

=(1+cos x)^2/(1-cos^2 x)

=(1+2cos x+cos^2 x)/sin^2 x

=1/sin^2 x+2cos x/sin^2 x+cos^x/sin^2 x

=cosec^2 x+2cosec x.cot x+cot^2 x

Let,I=int(cosec^2 x+2cosec x.cot x+cosec^2 x-1)

or,I=2intcosec^2 x dx+2int cosecx.cotx dx-intdx

or,I=2cot x+2 cosec x+x+c