Question
Download Solution PDFIf f(x) = \(\rm {2x\over {1\ +\ x^2}}\), then find the value of f(tan θ).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Trigonometric Formulae:
\(\rm \sin 2x = \frac{2\tan x}{1\ +\ \tan^2x}\)
\(\rm \cos 2x = \frac{1\ -\ \tan^2x}{1\ +\ \tan^2x}\)
\(\rm \tan 2x = \frac{2\tan x}{1\ -\ \tan^2x}\)
Calculation:
We have f(x) = \(\rm {2x\over {1\ +\ x^2}}\).
Substituting x = tan θ, we get:
⇒ f(tan θ) = \(\rm {2\tan\theta\over {1\ +\ \tan^2 \theta}}\) = sin 2θ.
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