More Trig (because I'm stupid) (1 Viewer)

[Average Boreduser]

How do you do these?

 

[Anaya R]

Still working out the first one, but for the second one try applying the fact that cos3x = cos(x+2x) and expand that. By doing so you'll be able to apply the sin2x and cos2x double angle identities

 

[Anaya R]

Ok with the first one you want to let theta=2x. (The implication is that theta/2 = x). Doing that will give you (sin2x+sinx)/(1+cos2x+cosx). If you expand the double angle identities and collect like terms, you'll be able to cancel out some stuff to get sinx/cosx. That is equal to tanx. You can then sub in theta/2 and tan theta/2 = t.

 

[Average Boreduser]

Hi Thanks so much

 

[aim for 95+]

Q2wish my handwriting is not so bad to understand.

Good luck Tomorrow

 

[Drongoski]

No. You're not stupid. It took me a while to do it. Not that straightforward.

You can derive, if necessary, that: 2sinAsinB = cos(A-B) - cos(A+B) from:

cos(A+B) = cosAcosB - sinAsinB and cos(A-B) = cosAcosB + sinAsinB




QED

 

[5uckerberg]

For the question , we can start like this

.

This just becomes



Simplifying we have



Factorising it becomes