Question

Prove identity trigonometric equation


`2 \tan(x) = ( \cos(x) )/( \csc(x - 1) ) + ( \cos(x) )/( \csc(x + 1) )`
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Answer 1

Step-by-step explanation:

The given equation is False, so cannot be proven to be true.

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Perhaps you want to prove ...

`2tan(x)=\frac{cos(x)}{\csc{(x)}-1}+\frac{cos(x)}{\csc{(x)}+1}`

This is one way to show it:

`2tan(x)=cos((x))\frac{(\csc{(x)}+1)+(\csc{(x)}-1)}{(\csc{(x)}-1)(\csc{(x)}+1)}\\\\=cos((x))\frac{2\csc{(x)}}{\csc{(x)}^2-1}=2cos((x))\frac{\csc{x}}{\cot{(x)}^2}=2(cos((x))sin((x))^2)/(cos((x))^2sin((x)))\\\\=2(sin(x))/(cos(x))\\\\2tan(x)=2tan(x)\qquad\text{QED}`

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We have used the identities ...

csc = 1/sin

cot = cos/sin

csc^2 -1 = cot^2

tan = sin/cos