Proof of inverse trigonometric identities

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Homework Help Overview

The problem involves proving the identity arcsin(1/sqrt(5)) + arcsin(2/sqrt(5)) = Pi/2, which falls under the subject area of inverse trigonometric functions.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants suggest taking the sine of the left-hand side to compare it with sin(Pi/2). Others propose analyzing each term individually and drawing a right triangle to visualize the relationships between the angles and their sine values.

Discussion Status

There are multiple lines of reasoning being explored, including geometric interpretations and trigonometric identities. Some participants have offered hints and guidance without providing direct solutions, indicating a collaborative effort to understand the problem.

Contextual Notes

Participants are encouraged to use geometric methods, such as drawing triangles and applying the Pythagorean theorem, while maintaining a focus on the relationships between the angles involved.

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

ehild
 
seboastien said:

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?
 
seboastien said:

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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