Answer:
We can use the chain rule to find the derivative of y with respect to x.
The chain rule states that if y = f(u) and u = g(x), then dy/dx = dy/du * du/dx
y =sin x sec (90-x)
dy/dx = cos x sec (90-x) * d/dx(sec (90-x)) - sin x tan (90-x) sec (90-x) * d/dx(90-x)
let us calculate the second derivative
du/dx = -cos(90-x)
d²y/dx² = -sin x sec (90-x) * cos (90-x) - cos x tan (90-x) sec (90-x) * cos (90-x) - cos x sec (90-x) * (-sin (90-x))
= -sin x sec (90-x) * cos (90-x) - cos x tan (90-x) sec (90-x) * cos (90-x) + cos x sec (90-x) * sin (90-x)
= -sin x sec (90-x) * cos (90-x) + cos x tan (90-x) sec (90-x) * sin (90-x)
= -(sin^2 x + cos^2 x) sec (90-x) tan (90-x)
= -sec^2 (90-x) tan (90-x)
So, the value of the second derivative of y with respect to x is -sec^2 (90-x) tan (90-x)
Explanation: