Prove that `(tanx+cotx)^2=sec^2x+csc^2x`

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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.

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