prove that (tanx+cotx)^4=sec^4x csc^4x

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The identity `(tan x + cot x)^4 = sec^4 x*csc^4 x` has to be proved.

`(tan x + cot x)^4`

`tan x = sinx/cos x` and `cot x = cos x/sin x`

=> `(sin x/cos x + cos x/sin x)^4`

=> `((sin^2 x + cos^2 x)/(sin x*cos x))^4`

`sin^2x +...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

The identity `(tan x + cot x)^4 = sec^4 x*csc^4 x` has to be proved.

`(tan x + cot x)^4`

`tan x = sinx/cos x` and `cot x = cos x/sin x`

=> `(sin x/cos x + cos x/sin x)^4`

=> `((sin^2 x + cos^2 x)/(sin x*cos x))^4`

`sin^2x + cos^2x = 1`

=> `1/(sin x*cos x)^4`

=> `1/(sin^4 x*cos^4x)`

=> `sec^4x*cosec^4x`

This proves `(tan x + cot x)^4 = sec^4 x*csc^4 x`

Approved by eNotes Editorial Team