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

7239 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The point P, (-1,4) lies on a circle C that is centered about the origin. Find the equation of the tangent to the circle at point P.


LOWER TIER a) Multiply the following out: (x+3)(x-4). b) Factorise the following equation into two bracket form: x^2+7x+12


Simultaneous Equation: 3x + y = -4 / 3x - 4y = 6


Using Pythagoras theorem to find side lengths of a triangle


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