First slide

Multiple and sub- multiple Angles

Question

If $f (\frac{2 \tan x}{1 + \tan^{2} x}) =$
$\frac{(\cos 2 x + 1) (\sec^{2} x + 2 \tan x)}{2}$ then $f (1) =$

Moderate

A

2
B

1
C

3
D

4

Solution

$f (\frac{2 \tan x}{1 + \tan^{2} x}) = \frac{2 \cos^{2} x {(1 + \tan x)}^{2}}{2}$
$= \frac{1 + \tan^{2} x + 2 \tan x}{1 + \tan^{2} x} = 1 + \frac{2 \tan x}{1 + \tan^{2} x}$
$∴ f (4) = 5$

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