`1+sinx + sin^2(x) + .... = 4+2sqrt3, 0ltxltpi, x!=pi, then x = `
1) `(pi)/(3), (pi)/(4)` 2) `(pi)/(4), (pi)/(6)` 3) `(2 pi)/(5), (pi)/(6)` 4) `(pi)/(3), (2 pi)/(3) `

(pi)/(4)+(2 pi)/(3)-(pi)/(6)

((pi)/(4))+((2 pi)/(3))-((pi)/(6))

If 4cos^(2)theta=3 then theta =---- 1) (pi)/(6),(5 pi)/(6) 2) (pi)/(4),(3 pi)/(4) 3) (pi)/(3),(2 pi)/(3) 4) +-(pi)/(2)

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)

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)]

The range of function f(x)=cot^(-1)x+sec^(-1)x+ cosec^(-1)x is (A) [(pi)/(2), pi)uu(pi, (3 pi)/(2)] (B) ((pi)/(2), (3 pi)/(4)] uu [(5 pi)/(4), (3 pi)/(2)) (C) ((pi)/(2), pi)uu(pi ,(3 pi)/(2)) (D) ((pi)/(2), (3 pi)/(2))

The solutions of the equation sin x+2sin2x+sin3x=cos x+3cos2x+cos3x in the interval 0<=x<=2 pi, are (pi)/(8),(5 pi)/(8),(2 pi)/(3)(b)(pi)/(8),(5 pi)/(8),(9 pi)/(8),(13 pi)/(8)(1 pi)/(3),(9 pi)/(3),(2 pi)/(3),(13 pi)/(8) (d) (pi)/(8),(5 pi)/(8),(9 pi)/(3),(4 pi)/(3),(4 pi)/(3),(9 pi)/(3),(2 pi)/(3),(13 pi)/(8)(d)

The solution set of the equation 4s int h eta cos theta-2cos theta-2sqrt(3)s int_(h eta)+sqrt(3)=0 in the interval (0,2 pi) is {(3 pi)/(4),(7 pi)/(4)} (b) {(pi)/(3),(5 pi)/(3)}{(3 pi)/(4),pi,(pi)/(3)(5 pi)/(3)}(d){(pi)/(6),(5 pi)/(6),(11 pi)/(6)}

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

sin^(2)(pi)/(4)+sin^(2)(3 pi)/(4)+sin^(2)(5 pi)/(4)+sin^(2)(7 pi)/(4)=2