Grade 11Differential Calculus
Prove that the derivative of (sec x + tan x)/(sec x - tan x) is 2cos x/(1 - sin x)2
Prove that the derivative of (sec x + tan x)/(sec x - tan x) is 2cos x/(1 - sin x)2
1 Answer
Arun
Dear student
we can write it as
(sec x + tan x)2
hence its derivative =
2 (sec x + tan x) * (sec x tan x + sec2 x)
= 2 (1 + sinx )( 1 + sin x) / cos3x
= 2 (1 + sin x) / cos x ( 1- sinx)
= 2 (1 – sin2 x) / cos x ( 1 – sin x)2
= 2 cos x / (1- sin x)2
hope it helps
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