Let `lambda=tan((3pi)/4-1/4 sin^(-1)(-4/5)) then (lambda^2-lambda+22)^2 is`

tan^(-1)4+tan^(-1)5=cot^(-1)lambda, then find lambda

If tan((2 pi)/(3)-x)=(sin(2(pi)/(3)-sin2x))/(cos(2(pi)/(3)-cos2x)) where 0

Let alpha and beta be the values of x obtained form the equation lambda^(2) (x^(2)-x) + 2lambdax +3 =0 and if lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation alpha/beta + beta/alpha = 4/3 . then find the value of (lambda_(1)^(2))/(lambda_(2)) + (lambda_(2)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))

If alpha, beta are the roots of the equation lambda(x^(2)-x)+x+5=0 and if lambda_(1) and lambda_(2) are two values of lambda obtained from (alpha)/(beta)+(beta)/(alpha)=(4)/(5) , then (lambda_(1))/(lambda_(2)^(2))+(lambda_(2))/(lambda_(1)^(2)) equals

If tan 82(1)/(2^(@))=sqrt(lambda_(1))+sqrt(lambda_(2))+sqrt(lambda_(3))+2 then lambda_(1)+lambda_(2)+lambda_(3) is equal to

lim_(x->pi)(2-lambda/x)^(2tan((pipi)/(2lambda)))=1/e, then lambda is equal to -

Let plambda^(4)+qlambda^(3)+rlambda^(2) + slambda+t= |{:(lambda^(2)+3lambda,,lambda-1,,lambda+3),(lambda+1 ,,-2lambda,,lambda-4),(lambda-3,,lambda+4,,3lambda):}| be an indentity in lambda p,q, r s and r are constants. Then find the value of t.