tanα+cotα=sinα/cosα+cosα+sinα=(sin^2α+cos^2α)/cosαsinα=1/sinαcosα=2/sin2αsin^2α=(1-cos2α)/2cos^2α=(1+cos2α)/2sin^4α+cos^4α=[(1-cos2α)/2]^2+[(1+cos2α)/2]^2=1/2+1/2*cos^2(2α)=5/9...