Is cos(x)=(cot(x))/(csc(x)-sin(x)) ?

The answer to whether cos(x)=(cot(x))/(csc(x)-sin(x)) is False

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prove cos(x)=(cot(x))/(csc(x)-sin(x))

prove

cos (x) = \frac{cot ( x )}{csc ( x ) - sin ( x )}

False

Solution steps

cos (x) = \frac{cot ( x )}{csc ( x ) - sin ( x )}

Show that the two sides are not equal

For

cos (x) = \frac{cot ( x )}{csc ( x ) - sin ( x )}

plug in

x = 1

cos (1) = 0.54030 \dots

cos (1)

Refine to a decimal form

= 0.54030 \dots

\frac{cot ( 1 )}{csc ( 1 ) - sin ( 1 )} = 1.85081 \dots

\frac{cot ( 1 )}{csc ( 1 ) - sin ( 1 )}

Refine to a decimal form

= 1.85081 \dots

The two sides are not equal

\Rightarrow False

cos^{2} (2 x) = \frac{( 1 + cos ( 4 x ) )}{2}

\frac{1 + sin ( x )}{cos ( x ) tan ( x ) - 1} = - 1

\frac{sin ( x ) sec ( x )}{tan ( x )} = 1

cot (x) + 5 = 5 + csc (x) \cdot cos (x)

csc (θ) = cos (θ) cot (θ) + sin^{2} (θ) csc (θ)

Is cos(x)=(cot(x))/(csc(x)-sin(x)) ?
The answer to whether cos(x)=(cot(x))/(csc(x)-sin(x)) is False