Help with verifying trig identity: sin4t=4sintcos^3t - 4sin^3tcost

[94tank]

How can I verify
sin4t=4sintcos^3t - 4sin^3tcost

ive tried taking out 4 first and then 2 but that just leads me to get stuck.

ex
4(sintcos^3t) - (sin^3tcost)

 

[Harry_the_cat]

Start by fully factorising the RHS. The largest common factor is 4 sin t cos t. You should then see what to do next.

 

[94tank]

Start by fully factorising the RHS. The largest common factor is 4 sin t cos t. You should then see what to do next.

I took out the common factor and got the following.
4sincost(cos^2t-sin^2t)

i know now the trig identity there is cos2x but then that's where I get stuck.

 

[stapel]

I took out the common factor and got the following.
4sincost(cos^2t-sin^2t)

i know now the trig identity there is cos2x but then that's where I get stuck.

What do you mean by "4sincost"? Are you saying "4 sin(cos(t))"?

 

[Ishuda]

I took out the common factor and got the following.
4sincost(cos^2t-sin^2t)

i know now the trig identity there is cos2x but then that's where I get stuck.

The trig identities you need are
sin(2 u) = 2 sin(u) cos(u)
and
cos(2 u) = cos²(u) - sin²(u)

Although you can get those identities from the basic sum of angles trig identities, I think you will find it very helpful to have those particular trig identities memorized.

 

[Deleted member 4993]

I took out the common factor and got the following.
4*sin(t) * cos(t) * (cos^2(t)-sin^2(t))

i know now the trig identity there is cos2x but then that's where I get stuck.

Please pay attention to what you are writing! Sloppy work will get sloppy result!

4*sin(t) * cos(t) * [cos^2(t)-sin^2(t)]

= 2 * 2 * sin(t) * cos(t) * cos(2t)

= 2 * sin(2t) * cos(2t)

Continue.....