Question #e19c2

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Question #e19c2

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Answer 1 · 2017-10-05T03:42:41

It is a true trigonometric identity. There is nothing false about it.

Explanation:

$csc x = \frac{1}{sin x}$ $csc x=1/sin x$ and
$cot x = \frac{cos x}{sin x}$ $cot x=cos x/sin x$
Therefore

$\frac{csc x}{cot x} = sec x$ $Csc x/ cot x = sec x$
$\frac{\frac{1}{sin x}}{\frac{cos x}{sin x}} = sec x$ $(1/sin x)/(cos x/sin x)= sec x$
$\frac{1}{cos x} = sec x$ $1/cos x=sec x$
$sec x = sec x$ $sec x=sec x$

Answer 2 · 2017-10-05T03:56:58

Please see below.

Explanation:

An identity is an equation that is true for all values of the variable(s) for which both sides of the equation are defined.

$\frac{csc x}{cot x} = sec x$ $cscx/cotx = secx$ is true for all values of $x$ $x$ for which both sides are defined. So it is an identity.

For values of the form $x = π k$ $x = pik$ for integer $k$ $k$ , the left side is not defined and the right side is $\pm 1$ $+-1$ .

The phrase "false about the identity"is not at all clear. I can't really make sense of it.
I suspect that the intended question is more like: "For what values of $x$ $x$ do the expressions $\frac{csc x}{cot x}$ $cscx/cotx$ and $sec x$ $secx$ not give the same values?"

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Question #e19c2

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