" I."sin(x^(2)+5)

sin ^(2) 5 x

if I=int(x^(2)+20)/((x sin x+5cosx)^(2))dx ,then I equals-

If sin x=(sqrt(5))/(3) "and " .(pi)/(3) lt x lt pi find the values of (i) " sin " (x)/(2) " " (ii) " cos " (x)/(2) " " (iii) " tan " (x)/(2)

I= int ( sin 2 x)/( 1+ sin^(2) x) dx .

Find the the domain of following functions: (i) f(x)=sqrt(x^(2)-5) (ii) sin(x^(3)-x)

Find the the domain of following functions: (i) f(x)=sqrt(x^(2)-5) (ii) sin(x^(3)-x)

Find the maximum and the minimum values of the following function over R. (i) sin^(2) X (ii) 7 cos x -24 sin x + 5 (iii) 3 sin x-4 cos x (iv) 3 cos (4x -5) + 4 (v ) (sin x+ cos x) (vi) 5 sin x + 12 cosx + 13 (vii) (3 sin^(2) x+ 4) (ix) 5 sin x + 12 cos x -13

Evaluate : (i) " sin " (pi)/(2) " "(ii) " sin " (5pi)/(12)

Solve the following trigonometric equations, (i) 4 cos^(2)x+6"sin"^(2)x=5 (ii) 7 "sin"^(2)x+3 cos^(2)x=4 .