Is sin(α+β)-sin(α-β)=2cos(α)sin(β) ?

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

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prove sin(α+β)-sin(α-β)=2cos(α)sin(β)

prove

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

True

Solution steps

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

Manipulating right side

2 cos (α) sin (β)

Rewrite using trig identities

= sin (α + β) - sin (α - β)

We showed that the two sides could take the same form

\Rightarrow True

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

1 (- cos (2 x)) = 2 cos^{2} (x)

- tan^{2} (x) = (tan^{2} (x) + 1) (cos^{2} (x) - 1)

csc (x) tan (x) cos^{2} (x) = cos (x)

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

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