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Question

If 3f(tanx)+2f(cotx)=x+3, x(0,π2), then 15f(3)=
(correct answer + 1, wrong answer - 0.25)

A
4π+1
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B
4π+7
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C
2π+3
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D
2π+9
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Solution

The correct option is D 2π+9
3f(tanx)+2f(cotx)=x+3 (1)
Changing x to π2x, we get
3f(cotx)+2f(tanx)=π2x+3 (2)
From eqn(1) and (2), we have
f(tanx)=x+3π5
Now, at x=π3
f(3)=π3+3π5
15f(3)=5π+93π=2π+9

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