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

6937 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is 'e' and where does it come from?


Prove that 2 cot (2x) + tan(x) == cot (x)


How do I know which trigonometric identity to use in any given situation?


When using the addition rule in probability, why must we subtract the "intersection" to find the "union" with the Addition Rule?


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