Verify the following identity.
1 answer:
Recall the angle sum identities:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
sin(a + b) = sin(a) cos(b) + sin(b) cos(a)
sin(a - b) = sin(a) cos(b) - sin(b) cos(a)
Notice that adding the first two together, and subtract the last from the third, we get two more identities:
cos(a + b) + cos(a - b) = 2 cos(a) cos(b)
sin(a + b) + sin(a - b) = 2 sin(b) cos(a)
Let a = 4x and b = x. Then
cos(5x) + cos(3x) = 2 cos(4x) cos(x)
sin(5x) - sin(3x) = 2 sin(x) cos(4x)
Now,
as required.
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Answer:
Mr. devito needs to buy 40 packs
Step-by-step explanation:
Given:
Total number of fourth grade students = 118
The number of pencils in one pack = 6
The number pencil each student gets =2
To find:
The number of packs of pencils that is to be bought = ?
Solution:
To give all the 118 fourth grade students each 2 pencils , the total number of pencils needed will be
= >
=> 236 Pencils
We know that a pack contains 6 pencils, so the number of pack that has to be bought , in order to have 236 pencils will be
=>
On substituting the values
=>
=> 39.33
=> 40