Question

Please help :/ Express 2sin3theta sin5theta as an algebraic sum.

Answer 1

Use:

\[\large \color{green}{2\sin(\frac{C+D}{2})\sin(\frac{D-C}{2}) = \cos(C) - \cos(D)}\]

Answer 2

Here:

\[\frac{C+D}{2} = 3\]

\[\frac{D-C}{2} = 5\]

Solve them to find C and D here..

Answer 3

Ok, just a sec

Answer 4

\[C + D = 6\]

\[-C + D =1 0\]

Add them now you will get D..

Answer 5

16

Answer 6

Left hand side it will be:

2D = 16

Now find D from here..

Answer 7

8?

Answer 8

Yes..

Now you have D so find C now by plugging in D value in any one equation...

Answer 9

its looks like that double angle formula can be used.

Answer 10

\[C + D = 16 \implies C = 6 - D \implies C = 6 - 8 \implies C = -2\]

Answer 11

@muhammad9t5 which double angle will you use here ??

Answer 12

And do you know what question wants?/

It wants Algebraic Sum..

Meaning Plus or Minus separated terms..

Answer 13

So you will have now C = -2 and D = 8

\[\large \cos(-2) - \cos(8) \implies \color{green}{\cos(2) - \cos(8)}\]

\[\cos(- \theta) = \cos(\theta)\]

Answer 14

This will help. Here are the options:
a. -cos8theta+cos2theta
b. cos8theta-cos2theta
c. -cos2theta-cos2theta
d. cos8theta+cos2theta

Answer 15

How about first one ??

Answer 16

Yes, that's what I was thinking. @muhammad9t5 can you confirm?

Answer 17

\[\large \cos(-2\theta) - \cos(8 \theta) \implies \color{green}{\cos(2\theta) - \cos(8\theta)}\]

Answer 18

I confirm !

Answer 19

Yes, @waterineyes, perfect. hanks @Neemo. Thanks to everyyone who helped!

Answer 20

Welcome dear..

Interact when you are asked something @IloveCharlie

Answer 21

yw !

Answer 22

@waterineyes sorry it was sum to product identity..