Maharashtra State BoardHSC Science (Electronics) 11th
Advertisement Remove all ads

Prove the following: (1+tanx1-tanx)2=tan(π4+x)tan(π4-x) - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Prove the following:

`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`

Advertisement Remove all ads

Solution

R.H.S. = `tan(pi/4 + x)/(tan(pi/4 - x))`

= `(((tan  pi/4 + tan x)/(1 - tan  pi/4 tan x)))/(((tan  pi/4 - tan x)/(1 + tan  pi/4 tan x))) = (((1 + tanx)/(1 - (1)tan x)))/(((1 - tan x)/(1 + (1)tan x))`

= `((1 + tan x)/(1 - tan x)) xx ((1 + tan x)/(1 - tan x))`

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

= L.H.S.

Concept: Trigonometric Functions of Sum and Difference of Angles
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×