If `4 sin 27^@= sqrt(alpha+sqrt5)-sqrt(beta-sqrt5);(alpha,beta in I^+)` then `alpha+beta=`

If 4 sin 27^(@) = sqrt(alpha) + sqrt(beta) then the sum of the digits in (alpha + beta - alpha beta + 2)^(4)

If 4 sin 27^(@)=sqrt(alpha)-sqrt(beta) , then the value of (alpha+beta-alpha beta+2)^(4) must be

If 4 sin 27^(@)=sqrt(alpha)-sqrt(beta) , then the value of (alpha+beta-alpha beta+2)^(4) must be

If 4 sin 27^(@)=sqrt(alpha)-sqrt(beta) , then the value of (alpha+beta-alpha beta+2)^(4) must be

If sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, alpha beta in [0, pi] , then cos (alpha + beta) - cos (alpha - beta) is equal to -sqrt(k) . The value of k is _________.

If sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, alpha beta in [0, pi] , then cos (alpha + beta) - cos (alpha - beta) is equal to -sqrt(k) . The value of k is _________.

If sqrt2(sin alpha)/(sqrt(1+cos2 alpha))=1/7 and sqrt((1-cos2beta)/2)=1/(sqrt(10)) alpha, beta in (0, pi/2) then tan (alpha + 2 beta) is equal to _________

Show that the solution of the equation [(x, y),(z, t)]^(2)=O is [(x,y),(z,t)]=[(pm sqrt(alpha beta),-beta),(alpha,pm sqrt(alpha beta))] where alpha, beta are arbitrary.