may i have help?

Question

complete the identity: sec (t)- cos (t)=?

 

1.) -2tan^2(t)

 

2.) sin(t) tan(t)

 

3.) sec (t) csc (t)

 

4.) 1+ cos (t)

Answer 1

sec(t) = 1/cos(t)

 

substitute the right hand side of the above equation in the original equation:

 

1/cos(t)-cos(t)

 

common denominator would be cos(t)

 

(1-cos²(t))/cos(t)

 

we know that 1-cos²(t) = sin²(t)

 

so we'll have:

 

sin²(t)/cos(t) = sin(t)*(sin(t)/cos(t))

 

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

 

so the final answer would be #2...sin(t)*tan(t)