Is (sin(x))/(cos(x)+sin(x))=1 ?

The answer to whether (sin(x))/(cos(x)+sin(x))=1 is False

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prove (sin(x))/(cos(x)+sin(x))=1

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

\frac{sin ( 0 )}{cos ( 0 ) + sin ( 0 )} = 0

\frac{sin ( 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}

= 0

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= \frac{0}{1 + 0}

Simplify

= 0

The two sides are not equal

\Rightarrow False

p ro v e cos (x) = \frac{cot ( x )}{tan ( x )}

p ro v e cos^{2} (2 a) - sin^{2} (2 a) = cos (4 a)

p ro v e tan (2 x) - 2 cos (x) = 0

p ro v e cos^{2} (a) cot^{2} (a) = cot^{2} (a) - cos^{2} (a)

p ro v e cos (θ) = \frac{1}{2}

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