Prove that `cot((pi)/(20)).cot ((3pi)/(20)).cot ((5pi)/(20)).cot((7pi)/(20)).cot ((9pi)/(20)) =1`

Prove that cot(pi/4-2cot^(- 1)3)=7

Prove that cot(pi/4-2cot^(- 1)3)=7

cot((-15pi)/4)

Prove that: cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x)]=1

Find the exact value of the expression tan(pi/20)-tan((3pi)/20)+tan((5pi)/20)-tan((7pi)/20)+tan((9pi)/20).

Prove that: cos((3pi)/2+x)cos(2pi+x){cot((3pi)/2-x)+"cot"(2pi+x)}=1

Show that cot(pi/4+x)cot(pi/4-x)=1

Prove that cot^(-1)(13)+cot^(-1)(21)+cot^(-1)(-8)=pi .

Prove that: 15sin(5pi)/(12)+15cos(5pi)/(12)-20sin^3(5pi)/(12)-20cos(5pi)/(12)=0

Prove that : int_(0)^(pi//2) (dx)/(1+cot x)=(pi)/(4)