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Writing trigonometric functions as algebraic expressions

Write cos(arccosx + arctany) as an algebraic expression in x and y.

Solution Preview

First using cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
we can write
cos(arccosx+arctany)=
cos(arccosx)cos(arctany)-sin(arccosx)sin(arctany)
=xcos(arctany)-sqrt(1-x^2)sin(arctany)

Above I used cos(arccosx)=x and ...

Solution Summary

This shows how to translate a trigonometric function into an algebraic expression.

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