Prove that 12 cos(30°) - 2 tan(60°) can be written as √k where k is an integer, state the value of k.

Conversion of trigonometric functions:

cos(30°) = √3 / 2

tan(60°) = √3

Computing equation with trigonometric substitutions:

12 cos(30°) - 2 tan(60°) = 12 (√3 / 2) - 2 (√3) = (12 / 2) x √3 - 2√3 = 6√3 - 2√3 = 4√3

Rearranging into requested form:

4√3 = √42 x √3 = √16 x √3 = √48

Stating k:

√k = √48

k = 48

Answered by Nic D. Maths tutor

7232 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

There are 5 blue counters and 5 red. x takes 2 counters out of the bag without replacing them. What is the probability x took 2 red counters.


Solve the equations x-y=1 and 5x-3y=13


How do I factorise x^2 ​- 4?


Solve 5x^2 - 9x + 4 = 0 using the quadratic formula


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences