Determine whether it is TRUE or FALSE
1) cos(3u)-cos(u) = cos(2u)
2) cos^2(6v)-sin^2(6v)=cos(12v)
Since all you're asked is to determine whether they are true, just substitute
a random number for u and use your calculator and find out.
1) cos(3u)-cos(u) = cos(2u)
Make up something for u, such as u=37°
cos(3·37°)-cos(37°) = cos(2·37°)
cos(111°)-cos(37°) = cos(74°)
-.3583679495-.79863551 = .2756373558
-1.15700346 = .2756373558
So you know that one is FALSE.
-----------------------------
2) cos^2(6v)-sin^2(6v)=cos(12v)
Do the same:
cosē(6v)-sinē(6v)=cos(12v)
choose v as, say, 13°
cosē(6·13°)-sinē(6·13°)=cos(12·13°)
cosē(78°)-sinē(78°)=cos(156°)
.0432272712-.9567727288 = -.9135454576
-.9135454576 = -.9135454576
So you assume that one must be true since 13° is very arbitrary.
[In fact it is from a well-known identity:
cosē(q)-sinē(q) = cos(2q)
and it is what you have when q = 6v and 2q = 12v
Edwin