Stacked on some trigonometric trick i can't get on it. Please Help!

[AlexSendler100%]

Hello guys this problem is come when i solved one of my physics homeworks. I solved the physical part of the problem but then i stucked on some trigonometric trick i probably don't know and i cant get the finale result. They have got.

I attached photographs of the full solving please just ignore the physics part and help me with the last step of solving when is written. "It's Should be"

By the way i plug some numbers into the first form and the second form of the answer and i get the same value so the answer itself is definitely correct the problem is only in trigonometric identities.

 

[Deleted member 4993]

Hello guys this problem is come when i solved one of my physics homeworks. I solved the physical part of the problem but then i stucked on some trigonometric trick i probably don't know and i cant get the finale result. They have got.

I attached photographs of the full solving please just ignore the physics part and help me with the last step of solving when is written. "It's Should be"

By the way i plug some numbers into the first form and the second form of the answer and i get the same value so the answer itself is definitely correct the problem is only in trigonometric identities.

You need to divide the numerator and the denominator - by "same" trigonometric quantity .....

 

[AvgStudent]

[math]V^2=\frac{gR(\sin(\theta)-\mu_s\cos(\theta))}{\nabla^2(\blue{\cos(\theta)}+\mu_s\red{\sin(\theta)})}= \frac{gR(\tan(\theta)-\mu_s)}{\nabla^2(\blue{1}+\mu_s\red{\tan(\theta)})}[/math]What do you need to divide [imath]\cos(\theta)[/imath] to get 1 and what do you need to divide [imath]\sin(\theta)[/imath] by to get [imath]\tan(\theta)?[/imath] Do the same for the numerator

 

[AlexSendler100%]

Thanks you guys?