Find the minimum value of `4^(sin^(2x))+4^("cos"^(2x))`.

If alpha, beta are the roots of the quadratic equation x^(2)-2(1-sin 2theta) x-2 cos^(2) 2 theta=0, (theta in R) then find the minimum value of (alpha^(2)+beta^(2)) .

Find the value of sin(1/2cos^(-1)(-3/4))

Find the maximum and minimum values of x+sin2 x on [0,2 pi]

The minimum value of e^((2x^(2) - 2x + 1) sin^(2) x) is a)e b) 1//e c)1 d)0

Find the integral cos ^(4) 2 x

Find the value of int_0^(pi/2)sin^4x/(sin^4x+cos^4x)dx

The minimum value of function f(x) = 8^(sin^(-1)x)+8^(cos^(-1)x) is a) 2^(1+pi/4) b) 2^(-1+(3pi)/4) c) 2^(1+(3pi)/4) d) 2^(-1+(pi)/2)

If tan x^(circ)=(3)/(4), piltxlt(3 pi)/(2) , find the value of sin (x)/(2), cos (x)/(2) and tan (x)/(2) .

Find the derivative of x^4 ( 5 sin x - 3 cos x)

The minimum values of sin x + cos x is a) sqrt2 b) -sqrt2 c) (1)/(sqrt2) d) - (1)/(sqrt2)