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

prove that sqrt7+sqrt12gtsqrt6+sqrt13 .

(2+sqrt3)(2-sqrt3) is

Prove that sqrt i+sqrt(-i)=sqrt 2

Prove that 2cos(pi/16)=sqrt(2+sqrt(2+sqrt(2)))

Prove that tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2) .

Prove that sqrt7+sqrt6gtsqrt8+sqrt5 .

Prove that = h/sqrt(2mE) .

Prove that cot^(-1) ((sqrt(1+sin x) +sqrt(1-sin x))/(sqrt(1+sin x) -sqrt(1-sinx)))=(x)/(2), x in (0, (pi)/(4)) .

Prove that sqrt2+sqrt3 is irrational.

The A.M. of two positive numbers a and b is twice their G.M. Prove that - a:b=2+sqrt3:2-sqrt3 .