Question

Question #8331a

Answer 1

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