" sin "^(2)x+5cos^(2)x

int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)

int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)

Find the extreme values of the following function over R. (i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x) (ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x (v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x)

If /_\ = |[5+sin^(2)x,cos^(2)x,4sin2x],[sin^(2)x,5+cos^(2)x,4sin2x],[sin^(2)x,cos^(2)x,5+4sin2x]| =

int(cos x)/((4+sin^(2)x)(5-4cos^(2)x))backslash dx

The integral (sin^(2)xcos^(2)x)/((sin^(5)x+cos^(3)xsin^(2)x+sin^(3)xcos^(2)x+cos^(5)x)^(2))dx is equal to

int (sin ^ (2) x cos ^ (2) x) / ((sin ^ (5) x + cos ^ (3) x sin ^ (2) x + sin ^ (3) x cos ^ (2) x + cos ^ (5) x) ^ (2)) dx

Number of solutions to the equation 2^(sin^(2)x)+5.2^(cos^(2)x)=7, in the interval [-pi,pi], is