Let `Q=((cospi/4,-sinpi/4),(sinpi/4,cospi/4)) and x=((1/sqrt2),(1/(sqrt(2))))` then `Q^3X` is equal to

Let Q=({:(cos""pi/4,-sin""pi/4),(sin""pi/4, cos""pi/4):}) and X=({:(1/sqrt(2)),(1/sqrt(2)):}) then Q^(3)X is equal to

Let, P=({:(cos""pi/4, -sin""pi/4),(sin""pi/4, cos""pi/4):}) " and " x=({:(1/sqrt(2)),(1/sqrt(2)):}) . Then P^(3)X is equal to-

Let P=(("cos"(pi)/(4),-"sin"(pi)/(4)),("sin"(pi)/(4),"cos"(pi)/(4))) and X=(((1)/(sqrt(2))),((1)/(sqrt(2)))) . Then P^(3)X is equal to

Let Q = [{: (cos ""(pi)/(4) , - sin""(pi)/(4)),(sin""(pi)/(4), cos""(pi)/(4)):}] and x = [{:((2)/(sqrt(2))),((1)/(sqrt(2))):}] then Q^(3) x is equal to

If x = sqrt(7 - 4 sqrt(3)) , then x + (1)/(x) is equal to :

If z=cospi/4+isinpi/6 then

If f(x)=(x-4)/(2sqrt3) , then f'(1) is equal to?

If x=sqrt(2+sqrt(2)), then x^(4)+(1)/(x^(4)) is

Prove that: cospi/10-sinpi/10=sqrt(2)sin(3pi)/(20)

if alpha,beta be the roots of the equation x^(2)-px+q=0 and alpha>0,beta>0 then the value of alpha^((1)/(4))+beta^((1)/(4)) is (p+6sqrt(q)+4q^((1)/(4))sqrt(p+2sqrt(q)))^(k) where k is equal to