Question #8331a

1 Answer
Mar 20, 2016

As below

Explanation:

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