How do you prove the identity: `(tanx+cotx)^2=sec^2x csc^2x ?` ``
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We have to prove: `(tan x + cot x)^2 = sec^2 x + cosec^2x`
`sec^2x + cosec^2x`
=> `1/(cos^2 x) + 1/(sin^2 x)`
=> `(sin^2x + cos^2x)/(sin^2x*cos^2x)`
=> `1/(sin^2x*cos^2x)` ...(1)
`(tan x + cot x)^2`
=> `tan^2 x + cot^2x + 2*tan x*cot x`
=> `(sin^2x)/(cos^2x) + (cos^2x)/(sin^2x) + 2`
=> `(sin^4x + cos^4x)/(cos^2x*sin^2x) + 2`
=> `((sin^2x +...
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(tan x+cotx)^2 = (sinx/cosx + cosx/sinx)^2
= (sin^2 x + cos^x/(sinx cosx))^2
=(1/cosx. sinx)^2 [since sin^2x + cos^x= 1]
= (1/sinx . 1/cosx)^2
=(cosec x sec x)^2
= cosex ^2 x . sec ^2x
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