`lim_(x->pi/4)(tanx)^(tan2x)`

Match the following : {:("Column-I" , " Column - II"), ("(A)" lim_(x to pi/4)(sin2x)^(tan^(2)2x), "(p)" 1/2),("(B)" lim_(x to oo) ((2x-1)/(2x+1))^(x) , "(q)"e^(-1/2)),("(C)" lim_(x to pi/2)(tanx)^(tan 2x) , "(r)" e^(-1)),("(D)" lim_(x to pi/4) tan2x tan(pi/4-x), "(s)" 1):}

Match the following : {:("Column-I" , " Column - II"), ("(A)" lim_(x to pi/4)(sin2x)^(tan^(2)2x), "(p)" 1/2),("(B)" lim_(x to oo) ((2x-1)/(2x+1))^(x) , "(q)"e^(-1/2)),("(C)" lim_(x to pi/2)(tanx)^(tan 2x) , "(r)" e^(-1)),("(D)" lim_(x to pi/4) tan2x tan(pi/4-x), "(s)" 1):}

(lim)_(x->pi/2)(tan2x)/(x-pi/2)

(lim)_(x->pi/2)(tan2x)/(x-pi/2)

lim_(x->(pi/2)) (1-sinx)tanx =

lim_(x->(pi/2)) (1-sinx)tanx =

lim_(x->pi/4)(tan2(x-pi/4))/(x-pi/4)

Evaluate: lim_(x to pi/2) (sin x)^(tanx)

Find the following limits: lim_(xrarrpi/2)(tan3x-tanx)

lim_(x to pi/4)(tan^3x-tanx)/(cos(pi/4+x))=alpha and lim_(x to 0)(cosx)^cotx=beta .If alpha and beta are the roots of equation ax^2+bx-4 then ordered pair (a,b) is