" (1) "sqrt(12)2dos1 pi=(256)^(-4(3)/(2))

Simplify : (1)sqrt((256)^((1)/(4)))(2)(1)/(4)(128)^((1)/(3))

If z_(1)=sqrt(2)((cos pi)/(4)+i sin((pi)/(4))) and z_(2)=sqrt(3)((cos pi)/(3)+i sin((pi)/(3))) then |z_(1)z_(2)|=

The expression (tan^(4)x+2tan^(2)x+1)cos^(2)x, whenx =(pi)/(12) can be equal to (a)4(2-sqrt(3)) (b) 4(sqrt(2)+1) (c)16(cos^(2)pi)/(12) (d) 16(sin^(2)pi)/(12)

The integral int_(0)^( pi)sqrt(1+4sin^(2)((x)/(2))-4sin((x)/(2))dx) equal (1)pi-4(2)(2 pi)/(3)-4-4sqrt(3)(3)4sqrt(3)-4(4)4sqrt(3)-4-(pi)/(3)

Prove that (i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2) (ii) " 2 cos " (5pi)/(12) " cos " .(pi)/(12)=(1)/(2) (iii) " 2 sin ".(5pi)/(12) " cos " (pi)/(2) = ((2+sqrt(3))/(2))

Prove that (i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2) (ii) " 2 cos " (5pi)/(12) " cos " .(pi)/(12)=(1)/(2) (iii) " 2 sin ".(5pi)/(12) " cos " (pi)/(2) = ((2+sqrt(3))/(2))

The value of (1)/(sqrt(2))"sin"(pi)/(6)"cos"(pi)/(4)-"cot"(pi)/(3)"sec"(pi)/(6)+(5"tan"(pi)/(4))/("12sin"(pi)/(2)) is equal to

If z_(1)= sqrt(2)(cos ""(pi)/(4)+ isin""(pi)/(4))" and "z_(2)= sqrt(3)(cos ""(pi)/(3)+ isin"" (pi)/(3)) , then |z_(1)z_(2)| is

If the distance between the centers of two circles of unit radii is 1 the common area of the circles is 1) (2 pi)/(3)-sqrt(3) 2) (2 pi)/(3)+sqrt(3) 3) (2 pi)/(3)-(sqrt(3))/(2) 4) (2 pi)/(3)(sqrt(3))/(3)

Show that int_(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx = (1)/(2)-(sqrt(3))/(12)pi