Help with trig questions? compund angle formulas?

Question

Use the appropriate compound angle formulas ro develop the formula for
tan(2x).

Thanks a lot!

Answer 1

the appropriate compound angle formulas ro develop the formula for
tan(2x).

 = tan (2x)

{ Note : Double - Angle formuls are

 sin(2x) = 2sinxcosx    or    2tanx / (1+(tan^2)x)

cos(2x) = (cos^2)x - (sin^2)x       or         (1-(tan^2)x) / (1+(tan^2)x) }

⇒ tan2x = sin2x / cos2x

We know that sin(2x) = 2tanx / (1+(tan^2)x)   and  cos(2x) = (1-(tan^2)x) / (1+(tan^2)x)

⇒ tan2x = [ 2tanx / (1+(tan^2)x)] / [(1-(tan^2)x) / (1+(tan^2)x) ]

Note : (a/b) / (c/d) = (ad) / (bc)

⇒ tan2x = [ (2tanx)(1+(tan^2)x) ] / [ (1+(tan^2)x)(1-(tan^2)x) ]

Simplify

⇒ tan2x = [ 2tanx / (1-(tan^2)x)

Ther fore

⇒ tan2x = [ 2tanx / (1-(tan^2)x)