Is sin(a+b)-sin(a-b)=2cos(a)sin(b) ?

The answer to whether sin(a+b)-sin(a-b)=2cos(a)sin(b) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove sin(a+b)-sin(a-b)=2cos(a)sin(b)

prove

sin (a + b) - sin (a - b) = 2 cos (a) sin (b)

True

Solution steps

sin (a + b) - sin (a - b) = 2 cos (a) sin (b)

Manipulating right side

2 cos (a) sin (b)

Rewrite using trig identities

2 cos (a) sin (b)

Use the Product to Sum identity:

cos (s) sin (t) = \frac{1}{2} (sin (s + t) - sin (s - t))

= 2 \cdot \frac{1}{2} (sin (a + b) - sin (a - b))

Simplify

2 \cdot \frac{1}{2} (sin (a + b) - sin (a - b)) : sin (a + b) - sin (a - b)

2 \cdot \frac{1}{2} (sin (a + b) - sin (a - b))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2} (sin (a + b) - sin (a - b))

Cancel the common factor:

2

= (sin (a + b) - sin (a - b)) \cdot 1

Refine

= sin (a + b) - sin (a - b)

= sin (a + b) - sin (a - b)

= sin (a + b) - sin (a - b)

We showed that the two sides could take the same form

\Rightarrow True

Is sin(a+b)-sin(a-b)=2cos(a)sin(b) ?
The answer to whether sin(a+b)-sin(a-b)=2cos(a)sin(b) is True