" A bexample "2" if "(pi)/(2)

The value of (cos"" (pi)/(2)+isin ""(pi)/(2))(cos ((pi)/(2^2))+isin((pi)/(2^2))) (cos ((pi)/(2^3))+isin((pi)/(2^3)))" ………."oo is

The smallest positive root of the equation tan x-x=0 lies in (0,(pi)/(2)) (b) ((pi)/(2),pi)(pi,(3 pi)/(2)) (d) ((3 pi)/(2),2 pi)

Find the value of expression ((cos pi)/(2)+i sin((pi)/(2)))(cos((pi)/(2^(2)))+i sin((pi)/(2^(2))))......oo

tan^(-1)[(cos x)/(1+sin x)] is equal to (pi)/(4)-(x)/(2), for x in(-(pi)/(2),(3 pi)/(2))(pi)/(4)-(x)/(2), for x in(-(pi)/(2),(pi)/(2))(pi)/(4)-(x)/(2), for x in(-(pi)/(2),(pi)/(2))(pi)/(4)-(x)/(2), for x in(-(3 pi)/(2),(pi)/(2))

Prove that (i) " tan"^(2) .(pi)/(3) + 2cos^(2) .(pi)/(4)+ 3 sec^(2).(pi)/(6)+ 4 cos^(2).(pi)/(2)=8 (ii) " sin ".(pi)/(6) " cos 0 + sin ".(pi)/(4) " cos " .(pi)(4) + " sin " .(pi)/(3) "cos " .(pi)/(6) =(7)/(4) (iii) " 4sin " (pi)/(6) " sin"^(2) (pi)/(3) + 3 " cos " .(pi)/(3) " tan ".(pi)/(4) = " cosec"^(2).(pi)/(2)=4

Let f(x)={{:(-2sinx" if "xle-(pi)/(2)),(Asinx+B" if "-(pi)/2ltxlt(pi)/(2)),(cosx" if " xge(pi)/(2)):} . Then

The value of cos^(2)((pi)/(20))+cos^(2)((2 pi)/(20))+cos^(2)((3 pi)/(4))+......+cos^(2)((9 pi)/(20)) is

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