If `y=sin^(4)x+cos^(4)x` then `(y_(4)(0))/(8)` is equal to.

underset(x rarr0) Iim (sin^(2)(pi cos^(4)x)/(x^(4))) is equal to .

If y=y(x) and it follows the relation 4xe^(xy)=y+5sin^(2)x, then y'(0) is equal to

If y=(sin^(4)x-cos^(4)x+sin^(2) x cos^(2)x)/(sin^(4) x+ cos^(4)x + sin^(2) x cos^(2)x), x in (0, pi/2) , then

If y=e^(-x)cos x, then prove that y_(4)+4y=0

If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0,sin y),(0,1,0),(-sin y,0,cos y)] , then [F(x) G(y)]^(-1) is equal to

(cos^(4) x - sin^(4) x) is equal to

If (2+sin x)(dy)/(dx)+(y+1)cos x=0 and y(0)=1, then y((pi)/(2)) is equal to -(1)/(3)(2)(4)/(3) (3) (1)/(3)(4)-(2)/(3)

If cos x-cos y=0=sin x+sin y then sin(2020x)+sin(2020y) is equal to