Question

Write cos 9t-cos 7t as a product of two trigonometric functions of different frequencies.

Answer 1

you have formula for this: \[cos a - cos b = -2 sin\frac{a+b}{2}sin \frac{a-b}{2}\]
\(\text{so, yours is}\) \[cos(9t)-cos(7t)=-2sin\frac{9t+7t}{2}sin\frac{9t-7t}{2}\]
\(= -2sin(8t)sin(t)\)

Answer 2

Thanks a lot for the help. Can you answer my other question? I'll post it, wait a minute.

Answer 3

@Idealist

Answer 4

1+i . you have \(R= \sqrt{2}\) got that part?

Answer 5

Right. What's next?

Answer 6

if you have (1+1i) then take \(\sqrt {2} \) out, you have it forms\[\sqrt{2}\left((\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}\right)\]got this part?

Answer 7

Wait a minute, let me do the work, don't leave.

Answer 8

What do I do next?

Answer 9

other way, x =1, y =1. R = \(\sqrt{1+1}=\sqrt{2}\)
now, \(\frac{x}{R}= \frac{1}{\sqrt{2}}\)

Answer 10

that the way you got 1/sqrt2 inside, and then you have that is cos theta = 1/sqrt 2

Answer 11

so theta = pi/4

Answer 12

or theta = 7pi/4

Answer 13

now, the second term : i 1/sqrt 2 = y = sin theta, it tells us sin theta = pi/4, cannot be 7pi/4 which sin = -1/sqrt2

Answer 14

got this part?