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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

\frac{2 sin ( 0 ) cos ( 0 )}{cos ( 0 )} = 0

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

Simplify

= 0

The two sides are not equal

\Rightarrow False

tan (x - \frac{3 π}{2}) = - cot (x)

tan (\frac{1}{2} x) + cos (\frac{1}{2} x) = 2 csc (x)

sin (θ) \frac{cos ^{2} ( θ )}{sin ( θ )} = csc (θ)

\frac{tan ^{2} ( a ) + 1}{sec ( a )} = sec (a)

3 sin^{2} (2 x) \frac{1}{2} = \frac{3 cos ( 4 x )}{4}

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