Is (2cos(x))/(cos(x)+cos^2(x))=2 ?

The answer to whether (2cos(x))/(cos(x)+cos^2(x))=2 is False

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prove (2cos(x))/(cos(x)+cos^2(x))=2

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

\frac{2 cos ( 0 )}{cos ( 0 ) + cos ^{2} ( 0 )} = 1

\frac{2 cos ( 0 )}{cos ( 0 ) + cos ^{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{2 \cdot 1}{1 + 1 ^{2}}

Simplify

= 1

The two sides are not equal

\Rightarrow False

cos^{2} (x) (2 + tan^{2} (x)) = 2 - sin^{2} (x)

\frac{sec ( θ ) cos ( θ )}{cot ( θ )} = tan (θ)

sin^{2} (θ - α) = 1

sin (x) (1 + cos (2 x)) = sin (2 x) cos (x)

(sec (x) - tan (x)) (1 + sin (x)) = cos (x)

Is (2cos(x))/(cos(x)+cos^2(x))=2 ?
The answer to whether (2cos(x))/(cos(x)+cos^2(x))=2 is False