complete the proof of the identity by choosing the rule that justifies each step ofcos(x-y)/cosx cosy=1+tanx tany

Accepted Solution

To verify cos(x-y)/cosxcosy=1+tanxtany we proceed as follows:
cos (x+y)=cos x cos y-sin x sin y
considering left side we get
[cos(x+y)]/[cos x cos y]
=[cos x cos y-sin xsin y]/[cos x cos y]
=1-[sin x sin y]/[cos x cosy]
=1-[sin x/ cos x × sin y/ cos y]
=1-tan x tan y
 Hence the proof