Turn on thread page Beta
    • Political Ambassador
    • Thread Starter
    Offline

    20
    ReputationRep:
    Political Ambassador
    1) given that

    y= (1+tanx)/(1-tanx)

    where tanx does not = 1
    show that dy/dx is always positive

    I've differentiate and got (2sec^2x)/(1-tanx)^2

    but not sure how to prove that it's always positive
    • Community Assistant
    • Very Important Poster
    Offline

    20
    ReputationRep:
    Community Assistant
    Very Important Poster
    (Original post by ihatePE)
    1) given that

    y= (1+tanx)/(1-tanx)

    where tanx does not = 1
    show that dy/dx is always positive

    I've differentiate and got (2sec^2x)/(1-tanx)^2

    but not sure how to prove that it's always positive
    Probably more obvious if you transform the fraction into another form.
    Offline

    21
    ReputationRep:
    (Original post by ihatePE)
    1) given that

    y= (1+tanx)/(1-tanx)

    where tanx does not = 1
    show that dy/dx is always positive

    I've differentiate and got (2sec^2x)/(1-tanx)^2

    but not sure how to prove that it's always positive
    In the numerator, you have \sec x squared and in the denominator, you have 1-\tan x squared , so what does that tell you about the signs of the numerator and denominator?
    Offline

    11
    ReputationRep:
    (Original post by ihatePE)
    1) given that

    y= (1+tanx)/(1-tanx)

    where tanx does not = 1
    show that dy/dx is always positive

    I've differentiate and got (2sec^2x)/(1-tanx)^2

    but not sure how to prove that it's always positive
    What happens to a negative quantity when you square it?

    Edit: overlapped withDesmos
    • Political Ambassador
    • Thread Starter
    Offline

    20
    ReputationRep:
    Political Ambassador
    (Original post by Desmos)
    In the numerator, you have \sec x squared and in the denominator, you have 1-\tan x squared , so what does that tell you about the signs of the numerator and denominator?
    Thanks xox
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 12, 2017
Poll
Favourite type of bread
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.