Question #01fe8

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Question #01fe8

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Answer 1 · 2016-12-06T16:44:27

The equation cannot be verified. It is not true for all values of x.

Explanation:

An initial approach is to see if it is a trigonometric identity.
Starting with the left side and converting to sines and cosines,

$LS = SinXCosXCotX$
$LS = SinXCosX(CosX/SinX)$
$LS = (cancel SinX)cosX(CosX/(cancelSinX))$
$LS = Cos^2X$

The left side cannot equal the right side for all values of x since

$RS = CscX$
$RS = 1/SinX$

To prove it is not an identity, it is sufficient to find one value for x which does not satisfy both sides. For example, working in degrees, if x = 30 degrees,

$LS = Sin(30)Cos(30)Cot(30)$
$LS = (0.5)(0.866)(1.732)$
$LS = 0.750 (approx)$

$RS = Csc(30)$
$RS = 2$

Since the left side does not equal the right side for the value x = 30 degrees, the equation is not an identity and cannot be verified.

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Question #01fe8

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