f cos x=(-sqrt(15))/(4)" and "(pi)/(2)

If cos^(-1)((7)/(|x|))+cos^(-1)((4sqrt(15))/(|x|))=(pi)/(2) , then:

If cos^(-1)((7)/(|x|))+cos^(-1)((4sqrt(15))/(|x|))=(pi)/(2) , then:

f(x)= (sqrt2 cos x-1)/(cot x-1), x ne (pi)/(4) . If the function f(x) is continuous at x= (pi)/(4) then find f((pi)/(4))

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), the x -axis,and the ordinates x=(pi)/(4) and x=beta>(pi)/(4) is beta sin beta+(pi)/(4)cos beta+sqrt(2)beta Then f'((pi)/(2)) is ((pi)/(2)-sqrt(2)-1)( b) ((pi)/(4)+sqrt(2)-1)-(pi)/(2)( d) (1-(pi)/(4)-sqrt(2))

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

If the function f(x)=(sqrt(5+cos x)-2)/((pi-x)^(2)) is continuous at x=pi, find f(pi)

If the function f(x)=(sqrt(5+cos x)-2)/((pi-x)^(2)) is continuous at x=pi, find f(pi)