The given question seem incomplete
Rewrite the expression as a simplified expression containing one term
cos (α + β)cos(β) + sin( α + β)sin(β)
Answer:
The simplified form of the given expression is cos(α)
Step-by-step explanation:
We are given the expression
cos (alpha + beta)cos(beta) + sin( alpha + beta)sin(beta)
we will proceed by expanding the given expression as
(cos(alpha)cos(beta) - sin(alpha)sin(beta))cos(beta) + (sin(alpha)cos(beta)+cos(alpha)sin(beta))sin(beta)
cos(alpha)cos^2(beta) -sin(alpha)sin(beta)cos(beta) + sin(alpha)cos(beta)sin(beta) + cos(alpha)sin^2(beta)
The two middle terms will cancel each other so we are left with
cos(alpha)cos^2(beta) + cos(alpha)sin^2(beta)
cos(alpha)[cos^2(beta) + sin^2(beta)]
cos(alpha) (1) = cos(alpha) [cos^2(beta) + sin^2(beta) = 1]
Therefore the simplified form of the given expression is cos(α)
Answer:
Natasha £14
Peter £14
Malachy £28
Step-by-step explanation:
Add 1+1+2=4
56/4=14
Multiple each ratio by 14 check by adding up and see if its the beginning total figure!
Answer:
60
Step-by-step explanation:
Because the diameter of this circle is 20 and the formula for the circumference (perimeter) of a circle is pi * the diameter, or πd, which, if π is 3, can be computed as 60.
A takeaway from this problem is that you should memorize basic equations like the circumference/area of a circle.
Answer:
75%
Step-by-step explanation:
Percentage change = (change) ÷ (first value) × 100
Change = second value - first value = 56 - 32 = 24
∴ Percentage change = 
75%
