The identity to be solved is `(tan x + cot x)^2 = sec^2x + csc^2 x`

`(tan x + cot x)^2`

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

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

=> `1/(cos^2x*sin^2x)` ...(1)

`sec^2x + csc^2 x `

`=> 1/(sin^2x) +1/(cos^2x)`

=> `(cos^2x...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

The identity to be solved is `(tan x + cot x)^2 = sec^2x + csc^2 x`

`(tan x + cot x)^2`

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

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

=> `1/(cos^2x*sin^2x)` ...(1)

`sec^2x + csc^2 x `

`=> 1/(sin^2x) +1/(cos^2x)`

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

=> `1/(sin^2x*cos^2x)` ...(2)

**As (1) = (2), the identity `(tan x + cot x)^2 = sec^2x + csc^2 x` is proved.**