Question

Find principal value...

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Answer 1

Answer:

Let cos-1 (4 / 5) = x

cos x = 4 / 5 —- (i)

sin [(1 / 2) cos-1 (4 / 5)] = sin (x / 2) —- (ii)

From (i), cos x = 4 / 5

1 – 2 sin2 (x / 2) = 4 / 5

2 sin2 (x / 2) = 1 – (4 / 5) = 1 / 5

sin (x / 2) = √1 / 10