Given that 2cos(x+50)°=sin(x+40)° show tan x° = tan 40°/3

The formulae for the sum the sine and cosine of two angles are: 2(cos x°cos 50°- sin x°sin 50°)= sin x°cos 40°+cos x°sin 40°cos 50°= sin 40°sin 50° = cos 40° Therefore, 2 cos x°sin 40°- 2 sin x°cos 40° = sin x°cos 40°+cos x°sin 40°dividing by cos x gives:2 sin 40° - 2 tan x°cos 40° = tan x°cos 40° + sin 40°dividing by cos 40° gives:2 tan 40° - 2 tan x° = tan x° + tan 40°tan 40° = 3 tan x°1/3 tan 40° = tan x°#QED

Answered by Prashasti T. Maths tutor

6887 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I add up the integers from 1 to 1000 without going insane?


By using partial fractions, integrate the function: f(x) = (4-2x)/(2x+1)(x+1)(x+3)


Differentiate y= exp(cos^2(x)+sin^2(x)) by using the chain rule.


Given that f(x)= (4/x) - 3x + 2 find i) f'(x) and ii) f''(1/2)


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