This discussion is now closed.

Check out other Related discussions

- A level integration help
- RODS, RINGS AND STRINGS isaac physics
- BMO Prep
- Graphic calculator?
- Is there a rule of thumb of when to use integration by parts or substitution?
- Maths paper 2 igcse
- Engaa weighting
- Mat & step
- Losing confidence in Maths in year 13 doing further maths
- 2 cubes infused together
- trigs graph and solution
- A-Level Maths Proof question
- TMUA
- AL Maths Question-need some help!
- Advanced mathematics
- AQA A-level Further Maths Required Trig Functions?
- GCSE Edexcel Maths - trigonometric ratios of angles between 0 and 360
- Applied Calculus Help
- WJEC Unit 1 Maths As Level Discussion 15 May 2024
- Edexcel AS Maths Paper 1 (Pure)

Given that tan 75 = 2 + root 3, find in the form m + n root 3, where m and n are integers, the value of tan 15.

I can't get this one. There's another one which is tan 105 but I got that straight away, its - 2 - root 3. Can anyone tell me how to work out this problem please?

I can't get this one. There's another one which is tan 105 but I got that straight away, its - 2 - root 3. Can anyone tell me how to work out this problem please?

mik1a

Given that tan 75 = 2 + root 3, find in the form m + n root 3, where m and n are integers, the value of tan 15.

I can't get this one. There's another one which is tan 105 but I got that straight away, its - 2 - root 3. Can anyone tell me how to work out this problem please?

I can't get this one. There's another one which is tan 105 but I got that straight away, its - 2 - root 3. Can anyone tell me how to work out this problem please?

A start would be that a right angled triangle with another angle of 75 has third angle of 15, so begin by drawing said triangle...

Tan 15 = tan(75 - 60)

tan(75-60) = (tan 75 - tan 60)/(1 + tan75tan60)

tan60 = tan(30+30) = tan 30 + tan 30)/(1 - tan^2 30)

You should know that tan 30 = sqrt(1/3)

So tan 60 = 2sqrt(1/3)/(1-1/3) = 3sqrt(1/3) = sqrt(3).

tan 15 = (2 + sqrt 3 - sqrt3)/(1+3+2sqrt(3))

tan 15 = 2/(4+2sqrt3) = 1/(2 + sqrt3)

Rationalise the denominator to get

tan 15 = (2-sqrt3)/(4 - 3) = 2-sqrt3

tan(75-60) = (tan 75 - tan 60)/(1 + tan75tan60)

tan60 = tan(30+30) = tan 30 + tan 30)/(1 - tan^2 30)

You should know that tan 30 = sqrt(1/3)

So tan 60 = 2sqrt(1/3)/(1-1/3) = 3sqrt(1/3) = sqrt(3).

tan 15 = (2 + sqrt 3 - sqrt3)/(1+3+2sqrt(3))

tan 15 = 2/(4+2sqrt3) = 1/(2 + sqrt3)

Rationalise the denominator to get

tan 15 = (2-sqrt3)/(4 - 3) = 2-sqrt3

- A level integration help
- RODS, RINGS AND STRINGS isaac physics
- BMO Prep
- Graphic calculator?
- Is there a rule of thumb of when to use integration by parts or substitution?
- Maths paper 2 igcse
- Engaa weighting
- Mat & step
- Losing confidence in Maths in year 13 doing further maths
- 2 cubes infused together
- trigs graph and solution
- A-Level Maths Proof question
- TMUA
- AL Maths Question-need some help!
- Advanced mathematics
- AQA A-level Further Maths Required Trig Functions?
- GCSE Edexcel Maths - trigonometric ratios of angles between 0 and 360
- Applied Calculus Help
- WJEC Unit 1 Maths As Level Discussion 15 May 2024
- Edexcel AS Maths Paper 1 (Pure)

Latest

Trending

Last reply 4 days ago

AQA GCSE English Language Paper 1 (8700/1) - 23rd May 2024 [Exam Chat]Last reply 1 week ago

AQA A-Level Biology Paper 3 (7402/3) - 19th June 2024 [Exam Chat]Last reply 2 weeks ago

Free food on A-level results day 2024 (also Btec & GCSE) including Nando'sLast reply 3 weeks ago

AQA A-level Physics Paper 2 (7408/2) - 6th June 2024 [Exam Chat]Physics Exams

366

909

Last reply 3 weeks ago

SQA Results Day Chat / Post Your Results Thread 2024Last reply 3 weeks ago

Predict the 2024 Edexcel Maths grade boundaries correctly and win an Amazon voucher!Maths Exams

40

53

Last reply 3 weeks ago

A level+ 2024 Results Day Countdown - Hub is open! #FindYourFutureA-levels

191

792