Reduce Expression: a/(a2*sin2(t)+cos2(t))

[Curl]

I got this expression:

a / ( a²*sin(t)² + cos(t)² )

Is there any way to reduce it using some identity?

 

[sjb-2812]

I got this expression:

a / ( a²*sin(t)² + cos(t)² )

Is there any way to reduce it using some identity?

What is sin(t)² + cos(t)² ?

 

[Char. Limit]

What is sin(t)² + cos(t)² ?

Does that really matter, though? We're not dealing with sin^2(t)+cos^2(t). We're dealing with (a sin(t))^2 + cos^2(t).

 

[sjb-2812]

Does that really matter, though? We're not dealing with sin^2(t)+cos^2(t). We're dealing with (a sin(t))^2 + cos^2(t).

True, just trying a few things. Can we factor the bottom to give (sin²t + cos²t) x something? Might be useful, might not

 

[Char. Limit]

True, just trying a few things. Can we factor the bottom to give (sin²t + cos²t) x something? Might be useful, might not

Well, I don't know if it helps, but I managed to factor it to this:

$$\frac{a}{\left(a^2-1\right)sin^2(t) + 1}$$

That's the best I can do though.