Is 2sin(pi)=5sin(pi) ?

The answer to whether 2sin(pi)=5sin(pi) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove 2sin(pi)=5sin(pi)

prove

2 sin (π) = 5 sin (π)

True

Solution steps

2 sin (π) = 5 sin (π)

Manipulating left side

2 sin (π)

Simplify

2 sin (π) : 0

2 sin (π)

Simplify

sin (π) : 0

sin (π)

Use the following trivial identity:

sin (π) = 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

= 2 \cdot 0

Apply rule

0 \cdot a = 0

= 0

= 0

Manipulating right side

5 sin (π)

Simplify

5 sin (π) : 0

5 sin (π)

Simplify

sin (π) : 0

sin (π)

Use the following trivial identity:

sin (π) = 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

= 5 \cdot 0

Apply rule

0 \cdot a = 0

= 0

= 0

We showed that the two sides could take the same form

\Rightarrow True

tan (x) - \frac{1}{tan ( x )} = 2 sin^{2} (x) - 1

\frac{1}{cot ( u )} = \frac{cot ( u )}{1}

sin^{2} (x) \cdot sec (x) = tan^{2} (x)

1 + 2 sin (x) cos (x) = (sin (x) + cos (x))^{2}

sin (2 x) = 2 cos (x)