Question

Question #01fe8

Answer 1

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.