Is (cos(2x))/(cos(x)-sin(x))=2 ?

The answer to whether (cos(2x))/(cos(x)-sin(x))=2 is False

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prove (cos(2x))/(cos(x)-sin(x))=2

prove

\frac{cos ( 2 x )}{cos ( x ) - sin ( x )} = 2

False

Solution steps

\frac{cos ( 2 x )}{cos ( x ) - sin ( x )} = 2

Show that the two sides are not equal

For

\frac{cos ( 2 x )}{cos ( x ) - sin ( x )} = 2

plug in

x = 0

\frac{cos ( 2 \cdot 0 )}{cos ( 0 ) - sin ( 0 )} = 1

\frac{cos ( 2 \cdot 0 )}{cos ( 0 ) - sin ( 0 )}

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{cos ( 2 \cdot 0 )}{cos ( 0 ) - 0}

= \frac{cos ( 2 \cdot 0 )}{cos ( 0 ) - 0}

Simplify

= 1

The two sides are not equal

\Rightarrow False

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Is (cos(2x))/(cos(x)-sin(x))=2 ?
The answer to whether (cos(2x))/(cos(x)-sin(x))=2 is False