Determine the exact value of b such that csc (6b + pi/8) = sec (2b - pi/8)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to determine the value of b so that cosec (6b + pi/8) = sec (2b - pi/8)

cosec (6b + pi/8) = sec (2b - pi/8)

=> 1/sin(6b + pi/8) = 1/cos(2b - pi/8)

=> cos(2b - pi/8) = sin(6b + pi/8)

cos x = sin (pi/2 - x)

=> sin(pi/2 - 2b + pi/8) = sin(6b + pi/8)

=> pi/2 - 2b + pi/8 = 6b + pi/8

=> pi/2  = 8b

=> b = pi/16

The value of b = pi/16

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