math help (1 Viewer)

[B1andB2]

Hey, i'm struggling with this question:
Show that sin^27θ − sin^24θ = sin 11θ sin 3θ.
Appreciate it if someone could help me out!

 

[TheShy]

hopefully it's not too blurry,

 

[B1andB2]

View attachment 28288hopefully it's not too blurry,

Thank you so much!! May i ask how you got line 3?

 

[Pedro123]

That's just the difference of 2 squares, so

Here my stupid face was trying to simplify sin^(27)(θ)-sin^(24)(θ)

 

[B1andB2]

That's just the difference of 2 squares, so

Here my stupid face was trying to simplify sin^(27)(θ)-sin^(24)(θ)

It's meant to equal the RHS tho. I used difference of two squares but didn't know how to continue...

 

[Pedro123]

Sorry!

https://educationstandards.nsw.edu.au/wps/wcm/connect/d5e591b6-a549-4700-9f1e-5960913f6b60/mathematics-advanced-ext1-ext2-reference-sheet-nov2019.pdf?MOD=AJPERES&CVID=

Compound Angles section. Ask if you want a derivation

 

[TheShy]

I used difference of two squares but didn't know how to continue...

Once you used difference of two squares, use sum to product formula, then multiply them so that you can use double-angleformula to get rid of the theta/2

 

[Pedro123]

For reference, the formulas used are:

and

and then

 

[B1andB2]

Sorry!

https://educationstandards.nsw.edu.au/wps/wcm/connect/d5e591b6-a549-4700-9f1e-5960913f6b60/mathematics-advanced-ext1-ext2-reference-sheet-nov2019.pdf?MOD=AJPERES&CVID=

Compound Angles section. Ask if you want a derivation

Once you used difference of two squares, use sum to product formula, then multiply them so that you can use double-angleformula to get rid of the theta/2

For reference, the formulas used are:

and

and then

thank you for your help!