# Proof of inverse trigonometric identities

## Homework Statement

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

## The Attempt at a Solution

Can someone please give me so much as a hint?

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

ehild

dynamicsolo
Homework Helper

## 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?

PeterO
Homework Helper

## Homework Statement

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

## 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]