Homework Help

what is tan(tan^-1 2+tan^-1 1)?

user profile pic

jigsfix | Student, Undergraduate | (Level 3) eNoter

Posted January 6, 2012 at 9:17 PM via web

dislike 1 like

what is tan(tan^-1 2+tan^-1 1)?

2 Answers | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 6, 2012 at 9:47 PM (Answer #1)

dislike 1 like

You need to find `tan(tan^-1 2 + tan^-1 1),`  hence you need to use the formula:

`tan (alpha + beta) = (tan alpha + tan beta)/(1 - tan alpha*tan beta)`

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

You need to remember that `tan(tan^-1 a) = a`  such that:

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

`tan(tan^-1 2 + tan^-1 1) = 3/(1 - 2) =gt tan(tan^-1 2 + tan^-1 1) = -3.`

Hence, evaluating the value of tangent yields:  `tan(tan^-1 2 + tan^-1 1) = -3.`

user profile pic

lochana2500 | TA , Undergraduate | (Level 1) Valedictorian

Posted July 7, 2012 at 5:26 PM (Answer #2)

dislike 0 like

tan(tan⁻¹2+tan⁻¹1)

⇒ tan (A+B) = (tanA + tanB) / (1 - tanA.tanB)

= [tan(tan⁻¹2) + tan(tan⁻¹1)] / [1-tan(tan⁻¹2).tan(tan⁻¹1)]

⇒ tan(tan⁻¹x) = x

=(2+1)/(1-2*1)

= 3/-1

= -3

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes