Math Is Fun Forum

kathyhansen

Novice

Registered: 2024-05-07

Posts: 1

Help Me!

Hello everyone,

Prove that sin-1(3/5)+sin-1(5/13)=cos-1(33/65)

Many thanks in anticipation!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Help Me!

Hi kathyhansen,

Welcome to the forum.

There are two steps to do this.  Sin-1(3/5) is an angle (call it A)
  If you sketch a right angled triangle with hypotenuse 5 and opposite 3 then you can use pythag to get the adjacent and hence cos(A). Do the same for the other angle, I'll call it B.

Now use cos(A+B) on the left side of the identity and substitute the fractions (3/5 etc). Inverse cosine and you should get the right hand side of the expression.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Help Me!

Hi kathyhansen,

Welcome to the forum.

There are two steps to do this.  Sin-1(3/5) is an angle (call it A)
  If you sketch a right angled triangle with hypotenuse 5 and opposite 3 then you can use pythag to get the adjacent and hence cos(A). Do the same for the other angle, I'll call it B.

Now use cos(A+B) on the left side of the identity and substitute the fractions (3/5 etc). Inverse cosine and you should get the right hand side of the expression.

Bob

I notice that some people don't reply when you take time out to help out. This is not cool.