Is 3cos(x+y)+3cos(x-y)=6cos(x)cos(y) ?

The answer to whether 3cos(x+y)+3cos(x-y)=6cos(x)cos(y) is True

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prove 3cos(x+y)+3cos(x-y)=6cos(x)cos(y)

prove

3 cos (x + y) + 3 cos (x - y) = 6 cos (x) cos (y)

True

Solution steps

3 cos (x + y) + 3 cos (x - y) = 6 cos (x) cos (y)

Manipulating left side

3 cos (x + y) + 3 cos (x - y)

Factor

3 cos (x + y) + 3 cos (x - y) : 3 (cos (x + y) + cos (x - y))

= (cos (x + y) + cos (x - y)) \cdot 3

Manipulating right side

6 cos (x) cos (y)

Rewrite using trig identities

= 3 (cos (x - y) + cos (x + y))

We showed that the two sides could take the same form

\Rightarrow True

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

tan (x + \frac{π}{4}) = \frac{tan ( x ) + 1}{1 - tan ( x )}

csc (θ) cos (θ) tan (θ) = 1

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

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

Is 3cos(x+y)+3cos(x-y)=6cos(x)cos(y) ?
The answer to whether 3cos(x+y)+3cos(x-y)=6cos(x)cos(y) is True