Trig equation with supplementary angles

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Bruce

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Dec 15, 2014
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My teacher gave me old contests for extra credit, but I'm stuck on one. Evaluate without calculator, given that 3A and 4A are supplementary angles: 4 cos(A) - sec(2A).

I did differnt things-I changed sec(2A) to 1/cos(2A) and after more identities I saw cos(3A) term, so I changed it to -cos(4A). Next time I tried -cos(5A) for cos(2A), but everything I did went worse-not simpler. Am I trying the right kind of stuff here?

I think its not a super challenging contest so must be easier way. Thx :)
 
Bruce said:
My teacher gave me old contests for extra credit, but I'm stuck on one. Evaluate without calculator, given that 3A and 4A are supplementary angles: 4 cos(A) - sec(2A).

I did differnt things-I changed sec(2A) to 1/cos(2A) and after more identities I saw cos(3A) term, so I changed it to -cos(4A). Next time I tried -cos(5A) for cos(2A), but everything I did went worse-not simpler. Am I trying the right kind of stuff here?

I think its not a super challenging contest so must be easier way. Thx :)
Click to expand...
I suspect it is some manipulation of
-2 cos(7A) = 4 cos(A) - sec(2A)
but it really looks like a long drawn out process and I'm not going to try.
 
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