SOLUTION: Determine whether it is TRUE or FALSE 1) cos(3u)-cos(u) = cos(2u) 2) cos^2(6v)-sin^2(6v)=cos(12v)

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Question 978577: Determine whether it is TRUE or FALSE
1) cos(3u)-cos(u) = cos(2u)
2) cos^2(6v)-sin^2(6v)=cos(12v)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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.

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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