Question 919192
Search your table of trig identities to find
(1) tan(x+y) = (tan(x) + tan(y))/(1-tan(x)*tan(y))
Use your problem with x = 25 and y = 5, we get
(2) tan(30) = (tan(25) + tan(5))/(1-tan(25)*tan(5))
Answer: The trig expression is tan(30).
Proof that
(3) tan(x+y) = (tan(x) + tan(y))/(1-tan(x)*tan(y))
is as follows:
(4) tan(x+y) = sin(x+y)/cos(x+y) or using sin and cos of sums gives
(5) tan(x+y) = (sin(x)cos(y)+cos(x)sin(y))/(cos(x)cos(y)-sin(x)sin(y))
Now divide all four terms of (5) by cos(x)cos(y) and get
(6) tan(x+y) = (tan(x)+ tan(y))/(1-tan(x)tan(y)) QED