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Question

Statement I: lf f(θ)=cosθ1.cosθ2.cosθn, then the value of tanθ1+tanθ2++tanθn=f(θ)f(θ)
Statement II: Differential coefficient of the function f(g(x)) w.r.t function g(x) is f(g(x)).

Which of the above statements is/are correct?

A
Statement I only
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B
Statement II only
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C
Both I and II
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D
Neither I nor II
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Solution

The correct option is A Both I and II
I: f(θ)=cosθ1cosθ2cosθn
Differentiating both sides,
f(θ)=sinθ1cosθ2cosθncosθ1sinθ2cosθncosθ1cosθ2sinθn
Dividing f(θ) by f(θ), we get
f(θ)f(θ)=tanθ1tanθ2tanθ3tanθn
f(θ)f(θ)=tanθ1+tanθ2+tanθ3tanθn

II: d(f(g(x)))d(g(x))=d(f(g(x)))d(x)×d(x)d(g(x))=f(g(x))g(x)g(x)=f(g(x))

Both I and II are correct.

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