If `pi < 2theta < (3pi)/2`. then `sqrt(2+sqrt(2+2cos4theta))` 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)

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

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)

Find the Values of sin (pi/8) ,cos (pi/ 8) ,sec (pi/8) ,cosec (pi/8) ,tan (pi/8) and Cot (pi/8)

If sin2x + sin x = 0, then x is (A) n pi + (pi) / (3), 2n pi + (pi) / (6) (B) n pi, n pi + (- 1) ^ (n) ( pi) / (3) (C) n pi, 2n pi + 2 (pi) / (3), 2n pi-2 (pi) / (3) (D) 2n pi, n pi + 2 (pi) / ( 3)

If t a nalpha=5/2 , tanbeta=-7/9 where alpha in [pi/2,pi] , then alpha+beta lies in the interval. [(3pi)/2,(7pi)/3] (b) [(13pi)/6,(5pi)/2] [(13pi)/6,(7pi)/3] (d) [pi/6,pi/3]

if sin ((pi)/(4) cot theta ) = cos ((pi)/(4) tan theta ), then theta is equal to : a) 2 n pi + (pi)/(4) b) 2n pi pm (pi)/(4) c) 2 n pi - (pi)/(4) d) n pi + (pi)/(4)

The value of sin (pi/14)sin(3pi/14)sin(5pi/14)sin(7pi/14)sin(9pi/14)sin(11pi/14)sin(13pi/14) is?

If 3tan(theta-15^(@))=tan(theta+15^(0)), then theta is equal to n in Z ) pi pi+(pi)/(4) (b) n pi+(pi)/(8)n pi+(pi)/(3) (d) none of these