Homework Help

Show that sin 2x=2tan x/(1+tan^2x)?

user profile pic

she16 | Student, Undergraduate | (Level 1) eNoter

Posted August 16, 2011 at 2:57 PM via web

dislike 1 like

Show that sin 2x=2tan x/(1+tan^2x)?

2 Answers | Add Yours

user profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted August 16, 2011 at 3:01 PM (Answer #1)

dislike 0 like

We'll manage the LHS.

We'll write the formula that writes the sine of double angle in terms of sine and cosine of the angle.

sin 2x = 2 sin x*cos x

Now, we'll multiply and divide by cos x the right side, to create the tangent function:

sin 2x = 2 sin x*cos x*cos x/cos x

sin 2x = 2 tan x*`cos^(2)` x

But, from Pythagorean identity, we'll have:

1 + `tan^(2)` x = 1/`cos^(2)` x => `cos^(2)` x = 1/(1+`tan^(2)` x)

sin 2x = 2 tan x/(1 + `tan^(2)` x)

Therefore, the identity sin 2x = 2 tan x/(1 + `tan^(2)` x) is verified.

user profile pic

lochana2500 | TA , Undergraduate | (Level 1) Valedictorian

Posted July 5, 2012 at 3:39 PM (Answer #2)

dislike 0 like

L:H:S = sin2x

= 2sinx.cosx ÷ 1

Devide the numerator and denominator by cos²x

= (2sinx.cosx/cos²x) ÷ (1/cos²x) 

= 2sinx/cosx ÷ sec²x

= 2tanx ÷ (1+tan²x)

= R:H:S

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes