Proof of inverse trigonometric identities

  • Thread starter seboastien
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  • #1
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Homework Statement



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

Homework Equations





The Attempt at a Solution



Can someone please give me so much as a hint?
 

Answers and Replies

  • #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
 
  • #3
dynamicsolo
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Homework Statement



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

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?
 
  • #4
PeterO
Homework Helper
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58

Homework Statement



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

Homework Equations





The Attempt at a Solution



Can someone please give me so much as a hint?

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

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