Is sin(x)sin(2x)+cos(x)cos(2x)=cos(x) ?

The answer to whether sin(x)sin(2x)+cos(x)cos(2x)=cos(x) is True

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prove sin(x)sin(2x)+cos(x)cos(2x)=cos(x)

prove

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

True

Solution steps

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

Manipulating left side

sin (x) sin (2 x) + cos (x) cos (2 x)

Rewrite as

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

Rewrite using trig identities

cos (x) cos (2 x) + sin (x) sin (2 x)

Use the Angle Difference identity:

cos (s) cos (t) + sin (s) sin (t) = cos (s - t)

= cos (x - 2 x)

Simplify

cos (x - 2 x) : cos (x)

cos (x - 2 x)

Add similar elements:

x - 2 x = - x

= cos (- x)

Use the negative angle identity:

cos (- x) = cos (x)

= cos (x)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

45 - 25 sin (- 120 π t) = 45 + 25 sin (120 π t)

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

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

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

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

Is sin(x)sin(2x)+cos(x)cos(2x)=cos(x) ?
The answer to whether sin(x)sin(2x)+cos(x)cos(2x)=cos(x) is True