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
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