# Writing trigonometric functions as algebraic expressions

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

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##### Solution Summary

This shows how to translate a trigonometric function into an algebraic expression. The algebraic expressions are examined.

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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 ...

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