If ` tan^(-1) 4 + tan ^(-1) 5 = cot^(-1) lambda " , then find " 'lambda'`

If 2"tan"^(-1)(1)/(5)-"sin"^(-1)(3)/(5)= -"cos"^(-1)(63)/(lambda , then lambda=

If 2"tan"^(-1)(1)/(5)-"sin"^(-1)(3)/(5)= -"cos"^(-1)(63)/(lambda , then lambda=

If 2"tan"^(-1)(1)/(5)-"sin"^(-1)(3)/(5)= -"cos"^(-1)(9lambda)/(65) , then lambda=

If 2"tan"^(-1)(1)/(5)-"sin"^(-1)(3)/(5)= -"cos"^(-1)(9lambda)/(65) , then lambda=

Sometimes we are just concerned with finding integral solutions to equations. Consider the equation tan^(-1).(1)/m+tan^(-1).(1)/n=tan^(-1).(1)/lambda , where m,n, lambda in N If lambda is such that lambda^2=1 is a prime, then how many solutions (m,n) are there for the equation?

Sometimes we are just concerned with finding integral solutions to equations. Consider the equation tan^(-1).(1)/m+tan^(-1).(1)/n=tan^(-1).(1)/lambda , where m,n, lambda in N For lambda=11 , an integral pair (m,n) satisfying the equation is

Sometimes we are just concerned with finding integral solutions to equations. Consider the equation tan^(-1)(1/m)+tan^(-1)(1/n)=tan^(-1)(1/lambda) , where m, n, lambda in N For lambda=11 , an integral pair (m, n) satisfying the equation is:

Sometimes we are just concerned with finding integral solutions to equations. Consider the equation tan^(-1).(1)/m+tan^(-1).(1)/n=tan^(-1).(1)/lambda , where m,n, lambda in N How many positive integral solutions (m,n) exist for the equation if lambda=3 ?