Question
Sun September 27, 2009 By:

prove that : (1-tanx)Square +(1 - cotx)square = (secx -cosecx)square

Expert Reply
Sun September 27, 2009

(1 - tan x)2 + (1 - cot x)2 = 1 - 2tan x + tan2 x + 1 - 2cot x + cot2 x

= 1 + tan2 x - 2tan x + 1 + cot2 x - 2cot x

= sec2 x - 2(tan x + cot x) + cosec2 x

= sec2 x - 2sec x cosec x  + cosec2 x  

 { (tan x + cot x) = (sin x/cos x + cos x/sin x) = (sin2 x + cos2 x)/(sinx cosx) = sec x cosec x}

= (sec x - cosec x)2

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