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Proof of inverse trigonometric identities

  1. Aug 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that arcsin(1/sqrt(5)) + arcsine(2/sqrt(5)) = Pi/2

    2. Relevant equations



    3. The attempt at a solution

    Can someone please give me so much as a hint?
     
  2. jcsd
  3. Aug 14, 2011 #2

    ehild

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    Take the sine of the left-hand side and see if it is equal to sin(pi/2)

    ehild
     
  4. Aug 14, 2011 #3

    dynamicsolo

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    Look at each term individually. Each is the arcsine of a ratio, so each term is an angle.

    For the first term, if theta = arcsin(1/√5) , then sin(theta) = 1/√5 . Draw a right triangle with one angle being (theta) and having the side opposite (theta) equal to 1 and the hypotenuse equal to √5 . What is the side adjacent to (theta) equal to?

    Now, is there an angle in that triangle having a sine of 2/√5 ? If so, it would be an angle which is the arcsine of (2/√5) . Call it (phi) . What do (theta) and (phi) add up to?
     
  5. Aug 14, 2011 #4

    PeterO

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    Draw a triangle and use pythagorus. [Just hints, not answers]
     
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