Is sin(α+β)+sin(α-β)=2sin(α)cos(β) ?

The answer to whether sin(α+β)+sin(α-β)=2sin(α)cos(β) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove sin(α+β)+sin(α-β)=2sin(α)cos(β)

prove

sin (α + β) + sin (α - β) = 2 sin (α) cos (β)

True

Solution steps

sin (α + β) + sin (α - β) = 2 sin (α) cos (β)

Manipulating right side

2 sin (α) cos (β)

Rewrite using trig identities

= sin (α + β) + sin (α - β)

We showed that the two sides could take the same form

\Rightarrow True

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

2 sin (x) cos (x) = sin (2 x)

cos (x) tan^{2} (x) + cos (x) = sec (x)

1 - sin (x) = cos (x)

cos^{2} (x) csc (x) - csc (x) = - sin (x)

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