Is sin(θ)cos(φ)=(sin(θ+φ)+sin(θ-φ))/2 ?

The answer to whether sin(θ)cos(φ)=(sin(θ+φ)+sin(θ-φ))/2 is True

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prove sin(θ)cos(φ)=(sin(θ+φ)+sin(θ-φ))/2

prove

sin (θ) cos (φ) = \frac{sin ( θ + φ ) + sin ( θ - φ )}{2}

True

Solution steps

sin (θ) cos (φ) = \frac{sin ( θ + φ ) + sin ( θ - φ )}{2}

Manipulating right side

\frac{sin ( θ + φ ) + sin ( θ - φ )}{2}

Rewrite using trig identities

= sin (θ) cos (φ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

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

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

Is sin(θ)cos(φ)=(sin(θ+φ)+sin(θ-φ))/2 ?
The answer to whether sin(θ)cos(φ)=(sin(θ+φ)+sin(θ-φ))/2 is True