JEE Advanced | 2015Trigonometric EquationHard
Question
Let ƒ(x) = 7tan8x + 7tan6x − 3tan4x − 3tan2x for all x ∈ 
. Then the correct expression(s) is(are)
. Then the correct expression(s) is(are)Options
A.
B.
C.
D.
Solution
Given f(x) = (7 tan6 x - 3 tan2 x)sec2 x
∴
Using I.B.P.
= x.(tan7x - tan3x)0π/4 -
(tan7 x - tan3 x)dx
= -
tan3 x(tan2 x - 1)sec2 x dx
Put tanx = t
=
Also,
(7tan6 x - 3 tan2x) sec2 xdx = tan7 x - tan3 x|0π/4 = 0
∴
Using I.B.P.
= x.(tan7x - tan3x)0π/4 -
(tan7 x - tan3 x)dx= -
tan3 x(tan2 x - 1)sec2 x dxPut tanx = t
=
Also,
(7tan6 x - 3 tan2x) sec2 xdx = tan7 x - tan3 x|0π/4 = 0Create a free account to view solution
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