CBSE Class 11-science Answered
prove that : (1-tanx)Square +(1 - cotx)square = (secx -cosecx)square
Asked by | 27 Sep, 2009, 08:19: PM
Expert Answer
(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
Regards,
Team,
TopperLearning.
Answered by | 27 Sep, 2009, 09:21: PM
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