Is (cos(x)-tan(x))/(sin(x)-cot(x))=-1 ?

The answer to whether (cos(x)-tan(x))/(sin(x)-cot(x))=-1 is False

prove (cos(x)-tan(x))/(sin(x)-cot(x))=-1

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{cos ( 1 ) - tan ( 1 )}{sin ( 1 ) - cot ( 1 )} = - 5.10138 \dots

\frac{cos ( 1 ) - tan ( 1 )}{sin ( 1 ) - cot ( 1 )}

Refine to a decimal form

= - 5.10138 \dots

The two sides are not equal

\Rightarrow False

p ro v e \frac{1 + cot ( x )}{csc ( x )} = sin (x) cos (x)

p ro v e sin^{2} (θ - α) = cos (θ)

p ro v e cos (2 x) cos (2 x) = cos^{2} (2 x)

p ro v e cos^{2} (x) + cot^{2} (x) = cos^{2} (x) cot^{2} (x)

p ro v e sec^{2} (x) sin^{2} (x) = \frac{1}{cot ^{2} ( x )}

Is (cos(x)-tan(x))/(sin(x)-cot(x))=-1 ?
The answer to whether (cos(x)-tan(x))/(sin(x)-cot(x))=-1 is False