Asked by Anonymous

Write the expression as a single trigonometric functions:
cos 6x cosx - sin6x sin x




if you could do it step by step?


also... How do I prove that sin(90deg + theta) = cos(theta)??


also step by step so i may learn?
Answered by Steve
the important identity here is

cos(A+B) = cosAcosB - sinAsinB

So, it looks like you have

cos(6x+x) = cos 7x

You also know that

sin(A+B) = sinAcosB + cosAsinB
so,
sin(90+x) = sin90cosx + cos90sinx = 1*cosx = 0*sinx = cosx

Do lots of these, since they will come in handy later on.
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