trig equation help

[shelly89]

show that \(\displaystyle sinh3\theta = 3sinh\theta + 4sinh^{3} \theta \)

am a bit stuck,,.....


\(\displaystyle sinh3\theta \) = \(\displaystyle sinh (2\theta + \theta) = sinh2\theta cosh\theta + cosh2\theta sinh\theta \)

am stuck from these line onwards, any help appreciated.

 

[srmichael]

show that \(\displaystyle sinh3\theta = 3sinh\theta + 4sinh^{3} \theta \)

am a bit stuck,,.....


\(\displaystyle sinh3\theta \) = \(\displaystyle sinh (2\theta + \theta) = sinh2\theta cosh\theta + cosh2\theta sinh\theta \)

am stuck from these line onwards, any help appreciated.

What's the identity for \(\displaystyle sinh2\theta\) and \(\displaystyle cosh2\theta\)? Plug these in and proceed...

 

[shelly89]

What's the identity for \(\displaystyle sinh2\theta\) and \(\displaystyle cosh2\theta\)? Plug these in and proceed...

is it


\(\displaystyle sinh2\theta = 2sinh\theta cosh\theta \)

and for \(\displaystyle cosh2\theta = cosh^{2} - sinh^{2} \) ?

Are these correct ?

 

[srmichael]

is it


\(\displaystyle sinh2\theta = 2sinh\theta cosh\theta \)

and for \(\displaystyle cosh2\theta = cosh^{2} - sinh^{2} \) ?

Are these correct ?

Almost. \(\displaystyle cosh2\theta = cosh^{2}\theta + sinh^{2}\theta \)

 

[shelly89]

Almost. \(\displaystyle cosh2\theta = cosh^{2}\theta + sinh^{2}\theta \)

thanks, is that using 'osbourne's rule?