Divide the equation by sin2x and create a new identity sin2x

Divide the equation by sin^2(x) and create a new identity. sin^2(x)+cos^2=1

sin^2 x + cos^2 x = 1

dividing the equation by sin^2 x

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

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

cos x / sin x = cot x

1 / sin x = cosec x

hence the identity becomes

1 + cot^2 x = cosec^2 x