Who is asking: Student
Prove: arc cos4/5 + arc cos (-5/13) = arc cos (-56/65)
If theta1=arc cos4/5 and theta2=arc cos(-5/13) then theta1 is in the first quadrant and theta2 is in the second quadrant. Thus cos(theta1 + theta2)
= cos(theta1)cos(theta2)-sin(theta1)sin(theta2) = (4/5)(-5/13)-(3/5)(12/13)
=-56/65. Hence arc cos4/5 + arc cos (-5/13) = arc cos (-56/65.
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