Answer: The answer is ![\cos(x+y)=\cos x\cos y-\sin x\sin y.](https://tex.z-dn.net/?f=%5Ccos%28x%2By%29%3D%5Ccos%20x%5Ccos%20y-%5Csin%20x%5Csin%20y.)
Step-by-step explanation: We are to find the sum or the difference that could be used to prove the following identity:
![\cos(\pi+q)=-\cos q.](https://tex.z-dn.net/?f=%5Ccos%28%5Cpi%2Bq%29%3D-%5Ccos%20q.)
To prove the above identity, the following sum which results in a difference, will be appropriate
![\cos(x+y)=\cos x\cos y-\sin x\sin y.](https://tex.z-dn.net/?f=%5Ccos%28x%2By%29%3D%5Ccos%20x%5Ccos%20y-%5Csin%20x%5Csin%20y.)
The proof is as follows
![L.H.S.\\\\=\cos(\pi+q)\\\\=\cos \pi\cos q-\sin \pi\sin q\\\\=(-1)\cos q-0\times \sin q\\\\=-\cos q\\\\=R.H.S.](https://tex.z-dn.net/?f=L.H.S.%5C%5C%5C%5C%3D%5Ccos%28%5Cpi%2Bq%29%5C%5C%5C%5C%3D%5Ccos%20%5Cpi%5Ccos%20q-%5Csin%20%5Cpi%5Csin%20q%5C%5C%5C%5C%3D%28-1%29%5Ccos%20q-0%5Ctimes%20%5Csin%20q%5C%5C%5C%5C%3D-%5Ccos%20q%5C%5C%5C%5C%3DR.H.S.)
Thus, the answer is ![\cos(x+y)=\cos x\cos y-\sin x\sin y.](https://tex.z-dn.net/?f=%5Ccos%28x%2By%29%3D%5Ccos%20x%5Ccos%20y-%5Csin%20x%5Csin%20y.)
Answer:
the answer will be 0.8
Step-by-step explanation:
hard to explain
Answer:
x=54
Step-by-step explanation:
these two angles are supplementary to each other. this is because alternate interior angles are congruent, and 2x+42 degrees is supplementary to the alternate interior angle of x-24 degrees. so, we can add these two numbers up and set it equal to 180.
2x+42+x-24=180
3x+18=180
3x=162
x=54
if this question is asking for x, 54 is the answer. if it is asking for the angle measures, plug in 54 for x for each angle and solve.
Answer:
(b) √5
Step-by-step explanation:
The square root of an integer is rational if the integer is a perfect square. You probably know the first few perfect square integers are 1, 4, 9, 16, 25, 36, ...
The integer 5 is not on that list, so its square root will be irrational.
√5 is irrational
Answer:
x = -1/4
Step-by-step explanation:
3/x = -4 - 8
3/x = -12
x= -3/12
x= -1/4