Question

If f(x)=tanx then show that f(2x)= 2f(x)/1-(fx)^2​

Answer 1

Step-by-step explanation:

Given:-

f(x) = Tan x

To find:-

Show that : f(2x)= 2f(x)/1-(fx)^2

Solution:-

Given that : f(x) = Tan x

Now,

LHS:-

f(2x)

= Tan 2x

=> Tan(x+x)

We know that

Tan(A+B) = (Tan A+ Tan B) /(1- TanA TanB)

We have A = B=x

=> Tan(x+x) = (Tan x+Tan x)/(1-Tan x Tan x)

=> Tan 2x = 2 Tan x /(1-Tan^2 x)

=>2f(x)/[1-(f(x))^2]

=> f(2x) = 2f(x)/[1-(f(x))^2]

Answer:-

f(2x) = 2f(x)/[1-(f(x))^2] is true for the given problem.

Used formula:-

• Tan(A+B) = (Tan A+ Tan B) /(1- TanA TanB)

Answer 2

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