Is (tan(x+y)-tany)/(1+tan(x+y)tany) = tan(x)?

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

For two angles a and b tan(a - b) = (tan a - tan b)/(1 + tan a*tan b)

Now in (tan(x+y) - tan y)/(1 + tan(x+y)*tan y) take x + y as a and y as b

=> (tan a - tan b)/(1 + tan a*tan b)

This is the same as tan (a - b)

= tan(x + y - y)

= tan  x

This proves that (tan(x+y) - tan y)/(1 + tan(x+y)*tan y) = tan x

lochana2500's profile pic

lochana2500 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

L:H:S = [tan(x+y)-tany]/[1+tan(x+y)tany]

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

= tan(x+y-y)

= tan x

= R:H:S

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question