Match the following
Column I `" "` Column II
`cos(73pi)/4` `" "` p. `-1/(sqrt(3))`
`tan(1397pi)/6` `" "` q. 0
`sin(2pi007)/6` `" "` r. `1/(sqrt(2))`
`sin(10^4pi)` `" "` s. 1

if z = cos ""pi/4 + i sin""pi/6 then

Evaluate the following limits : Lim_( x to pi//6) (sin (x - pi/6))/(sqrt(3)/2 - cos x )

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):}

If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2) then f' ((pi)/(6)) =?

Evaluate the following: 1. sin^(-1)(s i n(2pi)/3) 2. cos^(-1)(c o s(7pi)/6) 3. tan^(-1)(t a n(2pi)/3)

prove that : cos(pi/12)-sin(pi/12)=1/(sqrt(2))

In each of the following cases find the period of the function if it is periodic. (i) f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))

Evaluate each of the following: sin^(-1)(sin(2pi)/3) (ii) cos^(-1)(cos(7pi)/6) (iii) tan^(-1)(tan(3pi)/4)

The value of sin^(-1)(-sqrt3/2)+cos^(-1)(cos\ (7pi)/6) is a. (5pi)/6 b. pi/2 c. (3pi)/2 d. none of these

If f (x) = sqrt(cos ec ^(2) x - 2 sin x cos x - (1)/(tan ^(2) x )) x in ((7pi)/(4), 2pi ) then f' ((11 pi)/(6))=