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