Question

write the expression as a single trigonometric function.....

sin 9x cos 3x - cos 9x sin 3x

Answer 1

Here, \(\sin9x \cos 3x - \cos 9x \sin 3x\)

Let 9x = a and 3x = b

\(\sin a \cos b - \cos a \sin b\)

Answer 2

That is an identity : \(\sin (a-b) = \sin a \cos b - \cos a \sin b\)

Answer 3

So we have :
\(\sin 9x \cos 3x - \cos 9x \sin 3x = \sin (9x-3x)\) = ?

Can you tell me now @kausarsalley ?

Answer 4

@kausarsalley ...?

Answer 5

\[\sin (9x -3x)= \sin 9x \cos 3x - \cos 9x \sin 3x\]

Answer 6

Yes, but can you simplify \(\sin(9x - 3x)\)?

Answer 7

no please.....

Answer 8

Can you simplify 9x-3x?

Answer 9

\(\color{blue}{9x-3x=?}\)

Answer 10

\[9x - 3x = 6x\]

Answer 11

Yes so \(\sin (9x-3x) = ?\)

Answer 12

sin 6x..

Answer 13

\[\checkmark\]

Answer 14

That's it. great work.

Answer 15

thank you both alot! :)

Answer 16

Not me, not me.

Answer 17

You're welcome.