Maxima and MinimaMedium
Question
The minimum value of a sec x + b cosec x, 0 < a < b, 0 < x < π/2 is-
Options
A.a + b
B.a2/3 + b2/3
C.(a2/3 + b2/3)3/2
D.None of these
Solution
y = a se cx + b cosec x
= a sec x tan x - b cosec x cot x
= 0
a secx tan x = b cosec x cot x
a sin3x = b cos3x
tan3x =
tan x =
x = tan-1
Minimum value
y = a sec x + b cosec x
y =
y =
y = (a2/3 + b2/3)3/2
= a sec x tan x - b cosec x cot x= 0a secx tan x = b cosec x cot x
a sin3x = b cos3x
tan3x =
tan x =
x = tan-1
Minimum value
y = a sec x + b cosec x
y =
y =
y = (a2/3 + b2/3)3/2
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