sin^2(t)tan^2(t)cos^2(t)

Question

sin²(t)tan²(t)cos²(t)=?

Answer 1

Using the identity   tan²(t) = sin²(t) / cos²(t) to simplify the expression.

 

sin²(t) * [ sin²(t) / cos²(t)] * cos²(t) =

 

 

cos²(t) cancel each other out.

 

sin⁴(t)

Answer 2

I assume the goal here is to simplify

 

sin²t tan²t cos²t

 

There's an identity to apply here.

 

tan²t = sin²t / cos²t

 

and if you apply this identity to the thing you want to simplify, cos²t drops out, and all you have left is

 

sin²t sin²t = sin⁴t

 

Cheers!