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35 votes
If cos A= 1/8 With A in QIV, find sec A/2
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User Arun T
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1 Answer

17 votes
17 votes

Recall the half-angle identity,

cos²(x/2) = (1 + cos(x))/2

The angle A terminates in the fourth quadrant, so 270° < A < 360°. Then the corresponding half-angle terminates in the second quadrant, since 135° < A/2 < 180°, so cos(A/2) < 0. This means

cos(A/2) = - √((1 + cos(A))/2) = -3/4

so that

sec(A/2) = 1/cos(A/2) = -4/3.

User Aslamhossin
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