Complete the identity: csc(t)-sin(t)= and [sin+cos(t)]^2/[1+2sin(t)cos(t)]

Question

Not understanding how to complete the identity on problems such as these.  Please help me learn how to do these.I have many other ones but I believe I can figure those out but these two I don't know where to start.

Answer 1

csc t - sin t

 

let's start off with that one

 

csc t = 1 / sin t

 

so we have

 

1 / sin t - sin t

 

= (1 - sin^2 t) / sin t

 

= cos^2 t / sin t

 

= cos t cot t