- #1
JBD2
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Homework Statement
Verify the possibility of an identity graphically. (Completed this part)
Then, prove each identity algebraically.
[tex]\dfrac{sinx+tanx}{cosx+1}=tanx[/tex]
Homework Equations
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]
[tex]cot\theta=\dfrac{cos\theta}{sin\theta}[/tex]
[tex]sin^{2}\theta+cos^{2}\theta=1[/tex]
[tex]tan^{2}\theta+1=sec^{2}\theta[/tex]
[tex]cot^{2}\theta+1=csc^{2}\theta[/tex]
The Attempt at a Solution
[tex]\dfrac{sinx+\dfrac{sinx}{cosx}}{cosx+1}[/tex]
[tex]\dfrac{sinx+sinxcosx}{cosx+1}[/tex]
[tex](sinx+sinxcosx)(cosx+1)[/tex]
[tex]sinxcosx+sinx+sinxcos^{2}x+sinxcosx[/tex]
[tex]\dfrac{sinxcos^{2}x}{sinx}+\dfrac{2sinxcosx}{sinx}+\dfrac{sinx}{sinx}[/tex]
[tex]cos^{2}x+2cosx+1[/tex]
[tex]1-sin^{2}x+2cosx+1[/tex]
[tex]2cosx-sin^{2}x+2[/tex]
That's as far as I got and now I have no idea what to do.