Question

If f(x)=2tanx/1+tan²x, then find f(π/4).​

Answer 1

Answer:

f(π/4)=1

Step-by-step explanation:

tan(π/4) = 1

Therefore,

$f(\pi/4)=(2tan(\pi/4))/(1+tan^2(\pi/4))=(2*1)/(1+1^2)=2/2=1$

Hope this helps. :)

Answer 2

If f(x) = 2tanx/1 + tan²x then f(π/4) = 1

Given :

$\displaystyle \sf{f(x) = \frac{2tanx}{1 + {tan}^{2}x } }$

To find :

$\displaystyle \sf{ f \bigg( \frac{\pi}{4} \bigg) }$

Solution :

Step 1 of 2 :

Write down the given function

Here the given function is

$\displaystyle \sf{f(x) = \frac{2tanx}{1 + {tan}^{2}x } }$

On simplification we get

$\displaystyle \sf{f(x) =sin 2x \: \: \: \bigg[ \: \because \:sin 2x = \frac{2tanx}{1 + {tan}^{2}x } \bigg] }$

Step 2 of 2 :

Find the value of f(π/4)

Putting x = π/4 we get

$\displaystyle \sf{ f \bigg( \frac{\pi}{4} \bigg) = sin \: 2\bigg( \frac{\pi}{4} \bigg) }$

$\displaystyle \sf{ \implies f \bigg( \frac{\pi}{4} \bigg) = sin \: \bigg( \frac{\pi}{2} \bigg)}$

$\displaystyle \sf{ \implies f \bigg( \frac{\pi}{4} \bigg) = 1}$

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