Prove that: `"tan"142""(1^0)/2=2+sqrt(2)-sqrt(3)-sqrt(6)`

Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

Prove that: "cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

Prove that tan [7(1)/(2)]^0 = (sqrt(3) - sqrt(2)) (sqrt(2) - 1) .

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).

Show that cot (142\ 1/2) ^@ = sqrt(2) + sqrt(3) - 2 - sqrt(6)

Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+\ sqrt(4))+1/(sqrt(4)+sqrt(5))+1/(sqrt(5)+sqrt(6))+1/(sqrt(6)+sqrt(7))+\ 1/(sqrt(7)+sqrt(8))+1/(sqrt(8)+sqrt(9))=2

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2. cos^(-1)x , 0

Prove that cot 7 ""(1^(@))/(2) = sqrt2 + sqrt3 + sqrt4 + sqrt6 = (sqrt3 + sqrt2) (sqrt2 +1 ).

Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1