To Prove (tanx+cotx)^4=csc^4 x cdot sec^4 x
LHS =(tanx+cotx)^4
write tanx and cot x in terms of sin and cos
LHS =(sinx/cosx+cosx/sinx)^4, simplify => ((sinx xxsinx+cosx xxcosx)/(cosx cdot sinx))^4 => ((sin^2x +cos^2x)/(cosx cdot sinx))^4, Use Identity sin^2x +cos^2x=1 => (1/(cosx cdot sinx))^4 by definition of sec and csc => (sec x cdotcscx)^4 => sec^4 x cdotcsc^4x =RHS