Answer:
See explanation
Step-by-step explanation:
Use formula
[tex]\cos (x+y)=\cos x\cos y-\sin x\sin y[/tex]
Substitute it into the first fraction:
[tex]\dfrac{\cos (x+y)}{\cos x\cos y}\\ \\=\dfrac{\cos x\cos y-\sin x\sin y}{\cos x\cos y}\\ \\=\dfrac{\cos x\cos y}{\cos x\cos y}-\dfrac{\sin x\sin y}{\cos x\cos y}\\ \\=1-\dfrac{\sin x}{\cos x}\cdot \dfrac{\sin y}{\cos y}\\ \\=1-\tan x\tany[/tex]
Consider the whole expression:
[tex]\dfrac{\cos (x+y)}{\cos x\cos y}+\tan x\tan y\\ \\=1-\tan x \tan y+\tan x\tan y\\ \\=1[/tex]
Done!
