`1/(2^2)tan(pi/(2^2))+1/(2^3)tan(pi/(2^3))+....` to `oo`

The value of lim_(n->oo) [tan(pi/(2n)) tan((2pi)/(2n))........tan((npi)/(2n))]^(1/n) is

Find the inverse of the function f:[-(pi)/(2)-"tan"^(_1)(3)/(2),(pi)/(2)-"tan"^(-1)(3)/(4)] to [-1,1], f(x)=3cosx+4sinx +7.

lim_(n to oo)(1)/(n)[tan.(pi)/(4n)+tan.(2pi)/(4n)+…..+tan.(n pi)/(4n)]

If S=tan^-1( 2.1/(2+1^2+1^4)) +tan^-1 (2.2/(2+2^2+2^4))+ tan^-1 (2.3/(2+3^2+3^4))+. upto infinite terms, then S equals. (A) pi (B) pi/2 (C) pi/3 (D) pi/4

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):}

Solve: tan ^ (-1)tan((2pi)/3))

"sin^(2)(pi)/(6)+cos^(2)(pi)/(3)-tan^(2)(pi)/(4)=-(1)/(2)"

The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x)) simplifies to

tan""(2pi)/(5)-tan""(pi)/(15)-sqrt3tan""(2pi)/(5)tan""(pi)/(15) is equal to

Evaluate : "tan"(2pi)/(9)+"tan"(pi)/(9) + sqrt(3) "tan"(2pi)/(9) "tan"(pi)/(9)