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Hello everyone,
Prove that sin-1(3/5)+sin-1(5/13)=cos-1(33/65)
Many thanks in anticipation!
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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
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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
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