Is cos(7a)+cos(a)=2cos(4a)cos(3a) ?

The answer to whether cos(7a)+cos(a)=2cos(4a)cos(3a) is True

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prove cos(7a)+cos(a)=2cos(4a)cos(3a)

prove

cos (7 a) + cos (a) = 2 cos (4 a) cos (3 a)

True

Solution steps

cos (7 a) + cos (a) = 2 cos (4 a) cos (3 a)

Manipulating left side

cos (7 a) + cos (a)

Rewrite using trig identities

cos (7 a) + cos (a)

Use the Sum to Product identity:

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

= 2 cos (\frac{7 a + a}{2}) cos (\frac{7 a - a}{2})

Simplify

2 cos (\frac{7 a + a}{2}) cos (\frac{7 a - a}{2}) : 2 cos (4 a) cos (3 a)

2 cos (\frac{7 a + a}{2}) cos (\frac{7 a - a}{2})

\frac{7 a + a}{2} = 4 a

\frac{7 a + a}{2}

Add similar elements:

7 a + a = 8 a

= \frac{8 a}{2}

Divide the numbers:

\frac{8}{2} = 4

= 4 a

= 2 cos (4 a) cos (\frac{7 a - a}{2})

\frac{7 a - a}{2} = 3 a

\frac{7 a - a}{2}

Add similar elements:

7 a - a = 6 a

= \frac{6 a}{2}

Divide the numbers:

\frac{6}{2} = 3

= 3 a

= 2 cos (4 a) cos (3 a)

= 2 cos (4 a) cos (3 a)

= 2 cos (4 a) cos (3 a)

We showed that the two sides could take the same form

\Rightarrow True

tan (x) sin (x) - sin (x) = 0

tan (a) = \frac{( sin ( a ) )}{cos ( a )}

cos (2 x) = sin (2 x)

cos (4 x) + 4 cos (2 x) + 3 = 8 cos^{2} (x)

\frac{3 sin ^{2} ( 2 x )}{2} = \frac{3 cos ( 4 x )}{4}

Is cos(7a)+cos(a)=2cos(4a)cos(3a) ?
The answer to whether cos(7a)+cos(a)=2cos(4a)cos(3a) is True