They are equivalent to each other
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.
Answer:
At least 13 chocolates must be removed
Step-by-step explanation:
If there are three flavors, the probability of drawing 1 would be: 1
1/3 = 0.333
Which means, that every 3 attempts, theoretically you should do 1 of each, but how they ask for 5 chocolates of each would be:
3 * 5 = 15
At least 15 chocolates must be extracted to theoretically guarantee 5 chocolates each, but how we are interested in knowing is that a single flavor has 5 chocolates, so we discard the last two chocolates that represent the other two flavors
Therefore, for there to be safely 5 chocolates of the same flavor, at least 13 chocolates must be removed.
Answer:
4 pieces 1/3 of a yard left over
