Question

Express cos6mcos2m as a sum or difference

Answer 1

The expression cos(6m)cos(2m) can be converted to a sum using the product-to-sum identity, resulting in ½[cos(8m) + cos(4m)].

Step-by-step explanation:

To express cos(6m)cos(2m) as a sum or difference, we can use a trigonometric identity. Specifically, the product-to-sum identities allow us to write the product of two cosine functions as the sum or difference of two cosine functions. The identity we will use is:

cos(a)cos(b) = ½[cos(a + b) + cos(a - b)]

Applying this identity to our expression gives:

cos(6m)cos(2m) = ½[cos(6m + 2m) + cos(6m - 2m)]
½[cos(8m) + cos(4m)]

Therefore, cos(6m)cos(2m) can be expressed as the sum ½[cos(8m) + cos(4m)].

Answer 2

Given :

An expression (cos 6m)(cos 2m) .

To Find :

We need to express it in terms as sum or difference.

Solution :

We know,

cos( A + B ) = cosA cos B - sin A sin B

cos( A - B ) = cosA cos B + sin A sin B

Adding both the equations we get :

2cos A cos B = cos( A + B) + cos( A - B )

or

cos A cos B = cos( A + B) + cos( A - B )/2

Putting value of A = 6m and B = 2m in above equation, we get :

(cos 6m)(cos 2m) = cos( 6m + 2m ) + cos( 6m - 2m )/2

(cos 6m)(cos 2m) = cos(8m) + cos(4m)/2

Hence, this is the required solution.