Write the trigonometric expression as an algebraic expression. cos(arcsinx-arctan2x)

DofotheroU 2021-09-16 Answered
Write the trigonometric expression as an algebraic expression. cos(arcsinxarctan2x)
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odgovoreh
Answered 2021-09-17 Author has 107 answers
1. Let u=arctan2x , then tanu=2x1=adjopp.
2. hyp=1+4x2
3. Then cosu=114x2=cos(arctan2x)
4. And sinu=2x14x2=sin(arctan2x)
5. Let v=arccosx , then cosv=x.
6. opp=1x2
7. Then sinv=1x21=sin(arccosx)
8. cos(arcsinxarctan2x)cos(arcsinx)cos(arctan2x)+sin(arcsinx)sin(arctan2x)=
=cos(arcsinx)cos(arctan2x)+xsin(arctan2x)=2x2+1x214x2
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