Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Basically I have no idea whatsoever how to answer this question:

    prove that cot (A+B) = cot A cot B -1 / cot A + cot B


    the answer is in the back of the book but i would love to know how to solve this so i can do it on my own next time. please help someone!
    Offline

    0
    ReputationRep:
    tan x = sin x / cos x
    so cot x = cos x / sin x
    start here
    Offline

    1
    ReputationRep:
    What do you know about the identity for  tan (A+B) and the relationship between  tan x and  cot x ?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Goldfishy)
    What do you know about the identity for  tan (A+B) and the relationship between  tan x and  cot x ?
    cot x is 1/tan maybe??
    Offline

    11
    ReputationRep:
    @IAmTheChosenOne you could do it like that but that would be long - just use the addition formula and the fact that the usual relation between tan and cot
    • Study Helper
    Offline

    17
    ReputationRep:
    Study Helper
    i would start by swapping cot by 1/tan then addition formula, then once simplified change back to cot
    • Thread Starter
    Offline

    0
    ReputationRep:
    even if i did replace cot (a+b) with 1/tan i would still be clueless :0
    Offline

    1
    ReputationRep:
    (Original post by scholarshipkid)
    cot x is 1/tan maybe??
    Yep - don't hesitate :yep: You can apply this to the the tan addition formula.

    If you do manage that, you might like to investigate similar identities. such as  sec (A+B) or  cosec (A+B) to prove that you know how to do it.
    • Thread Starter
    Offline

    0
    ReputationRep:
    so

    1/tan(a+b)

    where would i go from here?
    • Thread Starter
    Offline

    0
    ReputationRep:
    it confuses me because it's a fraction!!
    • Thread Starter
    Offline

    0
    ReputationRep:
    okay so now i've got:

    tan a + tan b / 1-tan a x tan b

    stuckkkk!
    Offline

    1
    ReputationRep:
    (Original post by scholarshipkid)
    even if i did replace cot (a+b) with 1/tan i would still be clueless :0
    If  tan (A+B) = \frac {x}{y}
    then  cot (A+B) = \frac {1}{tan (A+B)} = \left(\frac{x}{y}\right)^{-1} = \frac {y}{x}
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Goldfishy)
    If  tan (A+B) = \frac {x}{y}
    then  cot (A+B) = \frac {1}{tan (A+B)} = \left(\frac{x}{y}\right)^{-1} = \frac {y}{x}

    does cot a + b flip the fraction then?
    • Study Helper
    Offline

    16
    ReputationRep:
    Study Helper
    (Original post by scholarshipkid)
    does cot a + b flip the fraction then?
    Yes because cot is the reciprocal of tan.

    But you don't need to use this - you can prove it directly from the fact that cot X = cos X / sin X, so cot (A + B) = cos(A + B) / sin (A + B) and then use the usual sum formulae to expand these and rewrite in terms of cot A and cot B.

    Try this and see how you get on.
 
 
 
Poll
Cats or dogs?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.