Trigonometric EquationHard
Question
If f(0) = 0 = f″(0) and f″(x) = tan2x then f(x) is
Options
A.log sec x - 
B.log cos x +
C.log sec x +
D.log cos x -
Solution
f″(x) = sec2x - 1
Integrating f′(x) = tanx - x + c1
But f′(0) = 0 - 0 + c1 ⇒ c1 = 0
⇒ f′(x) = tanx - x
Again Integrating
f(x) = log secx -
+ c2 but f′(0) = 0
⇒ c2 = 0
⇒ f(x) = log sec x -
Integrating f′(x) = tanx - x + c1
But f′(0) = 0 - 0 + c1 ⇒ c1 = 0
⇒ f′(x) = tanx - x
Again Integrating
f(x) = log secx -
+ c2 but f′(0) = 0⇒ c2 = 0
⇒ f(x) = log sec x -
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