MATH SOLVE

3 months ago

Q:
# 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

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