Answer:
The work is in the explanation.
Step-by-step explanation:
The sine addition identity is:
.
The sine difference identity is:
.
The cosine addition identity is:
.
The cosine difference identity is:
.
We need to find a way to put some or all of these together to get:
.
So I do notice on the right hand side the 
and the 
.
Let's start there then.
There is a plus sign in between them so let's add those together:
![=[\sin(a+b)]+[\sin(a-b)]](https://tex.z-dn.net/?f=%3D%5B%5Csin%28a%2Bb%29%5D%2B%5B%5Csin%28a-b%29%5D)
![=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]](https://tex.z-dn.net/?f=%3D%5B%5Csin%28a%29%5Ccos%28b%29%2B%5Ccos%28a%29%5Csin%28b%29%5D%2B%5B%5Csin%28a%29%5Ccos%28b%29-%5Ccos%28a%29%5Csin%28b%29%5D)
There are two pairs of like terms. I will gather them together so you can see it more clearly:
![=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]](https://tex.z-dn.net/?f=%3D%5B%5Csin%28a%29%5Ccos%28b%29%2B%5Csin%28a%29%5Ccos%28b%29%5D%2B%5B%5Ccos%28a%29%5Csin%28b%29-%5Ccos%28a%29%5Csin%28b%29%5D)
So this implies:
Divide both sides by 2:
By the symmetric property we can write:
Answer:
A.)
H0: μ ≤ 31
H1: μ > 31
B.)
H0: μ ≥ 16
H1: μ < 16
C.)
Right tailed test
D.)
If Pvalue is less than or equal to α ; we reject the Null
Step-by-step explanation:
The significance level , α = 0.01
The Pvalue = 0.0264
The decision region :
Reject the null if :
Pvalue < α
0.0264 > 0.01
Since Pvalue is greater than α ; then, we fail to reject the Null ;
Then there is no significant evidence that the mean graduate age is more Than 31.
B.)
H0: μ ≥ 16
H1: μ < 16
Null Fluid contains 16
Alternative hypothesis, fluid contains less than 16
One sample t - test
C.)
Null hypothesis :
H0 : μ ≤ 12
. The direction of the sign in the alternative hypothesis signifies the type of test or tht opposite direction of the sign in the null hypothesis.
Hence, this is a right tailed test ; Alternative hypothesis, H1 : μ > 12
d.)
If Pvalue is less than or equal to α ; we reject the Null.
The temperature at 5 am was -3 degrees
12-15=-3
Answer:
y</= 2
Step-by-step explanation:
9 + 1 = 10
9 + 2 < 10
y = anything < 2
Answer:
$37.50
Step-by-step explanation:
50*.25=12.50
Take $50 - 12.50 = 37.50
