How to solve this?

Question

complete the identity: sin t/(1+sin t) - sin t/(1-sin)= ?

1.) sec (t) csc (t)

2.) sin (t) tan (t)

3.) 1 + cos (t)

4.) -2tan^2 (t)

Answer 1

the common denominator between these two terms is :

 

(1+sin(t))*(1-sin(t)) = 1-sin²(t) = cos²(t)

 

so for the numerator we'll have:

 

sin(t)(1-sin(t))-sin(t)(1+sin(t)) = -2sin²(t)

 

knowing that tan(t)=in(t)/cos(t), the final answer would be:

 

-2sin²(t)/cos²(t) = -2tan²(t)

 

which is the answer #4