Someone please help me, I've been stuck for hour on how to evaluate cot(t)tan(t)-sin(t)cos(t)

Question

The choices are:
A) sin^2(t)
b) sin(t)tan(t)
c) sec(t)csc(t)
d) tan(t)+1

Answer 1

cot(t)tan(t)-sin(t)cos(t)

cot(t)tan(t) = 1

sin(t) cos(t) = sin(t) * cos(t)/sin(t)

:: 1 - cos(t)

 

which may = tan(t) + 1

 

 

we know

tan(t) = sin(t) / cos(t)

cot((t) = cos(t) / sin(t)

cos(t) = 1/sec(t)

sin(t) = 1/csc(t)

csc(t) = 1/sin(t)

sec(t) = 1/cos(t)

tan(t) = 1/cot(t)

cot(t) = 1/tan(t)

 

 

 

Answer 2

I played with this for a while too, and wasn't able to reach any of the given choices.

I decided to just check using some known angle to see if any of the choices would work.

Using a calculator and 30 degrees, none of the choices has the same calculated value as the original formula.

Check to see if you have an error in the problem statement.

 

The best simplification I can find is 1- 0.5sin(2t).  This gives the same value as cot(t)tan(t)-sin(t)cos(t).

 

cot(t)tan(t) = 1  (one is the reciprocal of the other)

sin(2t) = 2sin(t)cos(t)

sin(t)cos(t) = 0.5sin(2t)

Answer 3

cot t tan t=sin t cost

implies cos t /sin t*sin t/cos t=sin t cos t

implies sec t cosec t=1