Problems on Tan2x Formula

Problem 1: If tan x = 3/4, find the value of tan 2x using the formula.

Solution:

We have, tan x = 3/4.

Using the formula we get,

tan 2x = 2 tan x/(1 – tan² x)

= (2 (3/4))/(1 – (3/4)²)

= (6/4)/(1 – 9/16)

= (6/4)/(7/16)

= 24/7

Problem 2: If tan x = 12/5, find the value of tan 2x using the formula.

Solution:

We have, tan x = 12/5.

Using the formula we get,

tan 2x = 2 tan x/(1 – tan² x)

= (2 (12/5))/(1 – (12/5)²)

= (24/5)/(1 – 144/25)

= (24/5)/(-119/25)

= -120/119

Problem 3: If sin x = 4/5, find the value of tan 2x using the formula.

Solution:

We have, sin x = 4/5.

Clearly cos x = 3/5. Hence we have, tan x = 4/3.

Using the formula we get,

tan 2x = 2 tan x/(1 – tan² x)

= (2 (4/3))/(1 – (4/3)²)

= (8/3)/(1 – 16/9)

= (8/3)/(-7/9)

= -24/7

Problem 4: If cos x = 12/13, find the value of tan 2x using the formula.

Solution:

We have, cos x = 12/13.

Clearly sin x = 5/13. 

Hence we have, tan x = 5/12.

Using the formula we get,

tan 2x = 2 tan x/(1 – tan² x)

= (2 (5/12))/(1 – (5/12)²)

= (5/6)/(1 – 25/144)

= (5/6)/(119/144)

= 120/119

Problem 5: If sec x = 17/8, find the value of tan 2x using the formula.

Solution:

We have, sec x = 17/8.

Find the value of tan x using the formula sec² x = 1 + tan² x.

tan x = √((289/64) – 1)

= √(225/64)

= 15/8

Using the formula we get,

tan 2x = 2 tan x/(1 – tan² x)

= (2 (15/8))/(1 – (15/8)²)

= (15/4)/(1 – 225/64)

= (15/4)/(-161/64)

= -240/161

Tan2x is a trigonometric function used to solve various trigonometric questions. Tan2x Formula is a double-angle identity in trigonometry and can be written as tan2x = sin 2x/cos 2x.

In this article, we have covered, Tan2x in Trigonometry, Tan2x Formula, its derivation and others in detail.