[" 16."(root(4)(9)sin^(-1)(1-x)-2sin^(-1)x=(pi)/(2),pi x(pi)/(4 pi)(pi)/(9 pi/8 pi)(3)/(6):],[[" (A) "0,(1)/(2)," (B) "1,(1)/(2)," (C) "0," (D) "(1)/(2)]]

int[sin^(2)((9 pi)/(8)+(x)/(4))-sin^(2)((7 pi)/(8)+(x)/(4))]dx

sin ^(2) (pi)/(18)+sin ^(2) (pi)/(9)+sin ^(2) (7 pi)/(18)+sin ^(2) (4 pi)/(9)=

int_(-(pi)/(4))^((pi)/(4))(2 pi+sin2 pi x)/(2-cos2x)dx

Prove that sin ""(pi)/(9) sin ""(2pi)/(9) sin ""( 3pi)/(9) sin ""(4pi)/(9) = (3)/(16).

If sin^(-1)x+sin^(-1)y=(2 pi)/(3) ,then the value of cos^(-1)x+cos^(-1)y is (A) (2 pi)/(3) (B) (pi)/(3) (C) (pi)/(2) (D) pi

Prove that tan^(-1)((cosx)/(1+sin x)) =(pi)/(4)-(x)/(2), x in (-(pi)/(2), (pi)/(2)) .

Prove that: (sin^(2)pi)/(18)+(sin^(2)pi)/(9)+(sin^(2)(7 pi))/(18)+(sin^(2)(4 pi))/(9)=2

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 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 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)