Question

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Answer 1

Step-by-step explanation:

1. sin^-1 x = y

Since the range of sine inverse function lies between -π/2 to π/2.

So, -π/2 ≤ sin^-1 x ≤ π/2

-π/2 ≤ y ≤ π/2

2. det[(B^-1)AB] = det (B^-1) det(A) det(B)

= det(B^-1) det(B) det(A)

= det(B^-1 B) det(A)

= det(I) det(A)

= det (A)

[det[(B^-1) B]= det(I)]

3. y= sec^-1 (x+1/x-1) + sin^-1 (x-1/x+1)

= cos^-1 (x-1/x+1) + sin^-1 (x-1/x+1)

= π/2. [sec^-1 (x) = cos ^-1 (1/x)]

We know, [sin^-1 x+cos^-1 x= π/2]

So, dy/dx = 0