Prove that (a) `5 lt sqrt5+5^(1/3) +5^(1/4)`

Prove that 2/5 lt log_(10) 3 lt 1/2 .

Prove that 2/5 lt log_(10) 3 lt 1/2 .

Prove that 2/5 lt log_(10) 3 lt 1/2 .

Prove that 2/5 lt log_(10) 3 lt 1/2 .

Prove that (12)/(3 + sqrt5 - 2 sqrt2) = 1 + sqrt5 + sqrt10 - sqrt2

Prove that: cos36^(@)=(sqrt(5)+1)/(4)

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (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 : cot^-1 3 + cosec^-1 sqrt5 = pi/4

Prove that sin 9^circ = 1/4 (sqrt(3 + sqrt5) - sqrt(5 - sqrt5)) .

Prove that tan^-1 (1/4) + tan^-1 (2/9) = 1/2 cos^-1 (3/5) = sin^-1(1/sqrt5)