tan alpha=-(1)/(4sqrt(3)-3sqrt(5))

If tan alpha=(sqrt(3)+1)/(sqrt(3)-1) then the expression cos2 alpha+(2+sqrt(3))sin2 alpha is

tan alpha=(sqrt(3)+1)/(sqrt(3)-1) then the expression cos2 alpha+(2+sqrt(3))sin2 alpha is

If A,B are acute angles such that tan(alpha+beta)=1,tan(alpha-beta)=(1)/(sqrt(3)) then tan4 alpha

If cos alpha=(1)/(sqrt(2)),sin beta=(1)/(sqrt(3)), show that tan((alpha+beta)/(2))cot((alpha-beta)/(2))=5+2sqrt(6) or 5-2sqrt(6)

If alpha=tan^(-1)((sqrt(3)x)/(2y-x)),beta=tan^(-1)((2x-y)/(sqrt(3y)))" then "alpha-beta=

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) (ii) (5+2sqrt(3))/(7+4sqrt(3)) (iii) (1+sqrt(2))/(3-2sqrt(2)) (2sqrt(6)-sqrt(5))/(3sqrt(5)-2sqrt(6)) (v) (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18)) (vi) (2sqrt(3)-sqrt(5))/(2sqrt(3)+3sqrt(3))

The value of {1/((sqrt(6) - sqrt(5))) + 1/((sqrt(5) + sqrt(4))) + 1/((sqrt(4) + sqrt(3))) - 1/((sqrt(3) - sqrt(2))) + 1/((sqrt(2) - 1))} is :

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

If sin alpha=(3)/(5),tan beta=(1)/(2) and (pi)/(2)