Simplify cost sint2 cost sint22csctsin2t to a single trig

Simplify (cos(t) + sin(t))^2 - (cos(t) - sin(t))^2/2csc(t)sin(2t) to a single trig function

Solution

(cost +sint)^2 - (cost -sint)^2/2csct*sin2t

expand the brackets in numerator:

[(cos^t +sin^2t +2sintcost) - (cos^t +sin^2t -2sintcost)]/2csct*2sintcost

4sintcost/csc*4sintcost

(cancelling the terms in num. and den.)

sint