Question

2cos7xcos5x-cos2x=??​

Answer 1

Ответ:

2cos (7x × cos (-5x)) - cos (2x) = 2cos (7x × cos (5x)) - cos (2x)

Answer 2

To simplify the expression 2cos(7x)cos(5x) - cos(2x), you can use the trigonometric identity:

cos(A)cos(B) = 1/2[cos(A + B) + cos(A - B)]

In your expression, A = 7x and B = 5x. Using the identity:

2cos(7x)cos(5x) = cos(7x + 5x) + cos(7x - 5x) = cos(12x) + cos(2x)

Now, you can substitute this back into your original expression:

2cos(7x)cos(5x) - cos(2x) = (cos(12x) + cos(2x)) - cos(2x)

Now, you can simplify further:

(cos(12x) + cos(2x)) - cos(2x) = cos(12x)

So, the simplified expression is:

2cos(7x)cos(5x) - cos(2x) = cos(12x)