complete the identity: cot(t) + tan(t)=

Question

I'm having trouble solving the above question, as well as the one below 

 

tan20+tan10/1-tan20tan10=

Answer 1

cot(t)+tan(t)=

cos(t)/sin(t)+sin(t)/cos(t)=

[cos²(t)+sin²(t)]/sin(t)cos(t)=

1/sin(t)(cos)t=

sec(t)csc(t)

 

(tan(20)+tan(10))/(1-tan(20)tan(10))=

tan(20+10)=

tan(30)  (if you want to go further...)

tan(30)=(1/2)/(√3/2)=(1/2)(2/√3)=1/√3=√3/3