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 D2π+9 3f(tanx)+2f(cotx)=x+3⋯(1) Changing x to π2−x, we get 3f(cotx)+2f(tanx)=π2−x+3⋯(2) From eqn(1) and (2), we have f(tanx)=x+3−π5 Now, at x=π3 f(√3)=π3+3−π5 ⇒15f(√3)=5π+9−3π=2π+9