" If "pi<=x<=2 pi" then "cos^(-1)(cos x)" is equal to ":-

pi/4 + pi - pi/3 - pi/6

The possible values of theta in (0, pi) such that sin (theta) + sin (4 theta) + sin (7 theta) = 0 are (1) (2 pi) / (9), (i) / (4 ), (4 pi) / (9), (pi) / (2), (3 pi) / (4), (8 pi) / (9) (2) (pi) / (4), (5 pi ) / (12), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (8 pi) / (9) (3) (2 pi) / (9 pi) ), (pi) / (4), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (35 pi) / (36) (4) (2 pi ) / (9), (pi) / (4), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (8 pi) / (9)

The principal value of tan^-1(-1) is [pi/4,-pi/4,pi-pi/4,pi+pi/4]

lim_ (x rarr pi) ((sin (pi-x)) / (pi (pi-x)))

For 0 cos^(-1)(sintheta) is true when theta belongs to (a) (pi/4,pi) (b) (pi,(3pi)/2) (c) (pi/4,(3pi)/4) (d) ((3pi)/4,2pi)

The polar form of (i^(255))^(3) is (cos pi)/(2)+i(sin pi)/(2)bcos pi+is in pi c*cos pi-i sin pi d(cos pi)/(2)-is in(pi)/(2)

The range of tan^(-1)((2x)/(1+x^2)) is a) [-pi/4,pi/4] b) (-pi/2,pi/2) c) (-pi/2,pi/4] d) [pi/4,pi/2]

-1lt cos(2x -(pi)/(3))lt(1)/(2) has solution set (A) x in ((pi)/(3)+2n pi, (5pi)/(3)+2n pi), n in I (B) x in ((pi)/(3)+2n pi, (2pi)/(3)+2n pi)uu((2pi)/(3)+2n pi, (2n+1)pi), n in I (C) x in ((pi)/(3)+2n pi, pi+2n pi)uu(pi+2n pi, (5pi)/(3)+2n pi), n in I (D) x in ((pi)/(3)+n pi, (2pi)/(3)+n pi)uu((2pi)/(3)+n pi, (n+1)pi), n in I

If cosec . (pi)/(32)+ cosec. (pi)/(16)+ cosec. (pi)/(8)+ cosec. (pi)/(4)+ cosec. (pi)/(2)= cot. (pi)/(k) , then the value of k is