Answer:
We have to prove
sin(α+β)-sin(α-β)=2 cos α sin β
We will take the left hand side to prove it equal to right hand side
So,
=sin(α+β)-sin(α-β) Eqn 1
We will use the following identities:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Putting the identities in eqn 1
=sin(α+β)-sin(α-β)
=[ sin α cos β+cos α sin β ]-[sin α cos β-cos α sin β ]
=sin α cos β+cos α sin β- sinα cos β+cos α sin β
sinα cosβ will be cancelled.
=cos α sin β+ cos α sin β
=2 cos α sin β
Hence,
sin(α+β)-sin(α-β)=2 cos α sin β
Answer:
Step-by-step explanation:
Let d represent the number of dimes. Then the number of quarters is 2d-3 and the total value of the coins is ...
0.10d + 0.25(2d-3) = 7.05
0.60d -0.75 = 7.05 . . . . . . . simplify
d = (7.05 +0.75)/0.60 = 13 . . . . add 0.75, divide by 0.60
2d-3 = 2·13 -3 = 23
Brandon has 23 quarters and 13 dimes.
The three inside angles of a triangle need to equal 180 degrees.
This means X = 180 - 43 - 59 = 78 degrees.
X and Z make a straight line that also needs to equal 180 degrees,
so Z = 180 - 78 = 102 degrees.
Y = 180 - 102 - 13 = 65 degrees.
Answer:
A.) 3
Step-by-step explanation:
You do the x1-x2 divided by y1-y2 method, I find that more effective for finding the solution. Hope this helps!
140 * .45 = 63
Add 140 and 63
2. 203 because you are adding 45% of 140 to increase it by 45%
Same with the other except subtraction
4. 15
I think this is right, I am not sure