Question

If f : R → R is defined by f(x) = $\frac{1- x^{2}}{1 + x^{2}}$ then show that f (tan θ) = cos 2θ.

Answer 1

Answer:

f(tan θ) = cos 2θ

Step-by-step explanation:

Given: f(x) = (1 - x²)/(1 + x²)

∴ f(tan θ):

= (1 - tan² θ)/(1 + tan² θ)

= [(1 - sin²θ/cos²θ)]/[1 + sin²θ/cos²θ]

= (cos²θ - sin²θ)/(cos²θ + sin²θ)

= (cos²θ - sin²θ)/1

= (cos²θ - sin²θ)

= 1 - sin² θ - sin²θ

= 1 - 2 sin²θ

= cos 2θ

Hope it helps!

Answer 2

Answer:

f( tan theeta) = Cos 2theeta

Step-by-step explanation:

In the attachment I have answered this problem.

See the attachment for detailed solution.

I hope this answer helps you