Answer: (a), (b), (c), and (d)
Step-by-step explanation:
Check the options
![(a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x](https://tex.z-dn.net/?f=%28a%29%5C%5C%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D%5Csin%20%5E2x%2B%5Ccos%20%5E2x%2B2%5Csin%20x%5Ccos%20x%5C%5C%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D1%2B2%5Csin%20x%5Ccos%20x%5C%5C%5CRightarrow%20%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D1%2B%5Csin%202x)
![(c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x](https://tex.z-dn.net/?f=%28c%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csin%203x%7D%7B%5Csin%20x%5Ccos%20x%7D%3D%5Cdfrac%7B3%5Csin%20x-4%5Csin%20%5E3x%7D%7B%5Csin%20x%5Ccos%20x%7D%5C%5C%5C%5C%5CRightarrow%203%5Csec%20x-4%5Csin%20%5E2x%5Csec%20x%5C%5C%5CRightarrow%203%5Csec%20x-4%5B1-%5Ccos%20%5E2x%5D%5Csec%20x%5C%5C%5CRightarrow%20%203%5Csec%20x-4%5Csec%20x%2B4%5Ccos%20x%5C%5C%5CRightarrow%204%5Ccos%20x-%5Csec%20x)
![(d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x](https://tex.z-dn.net/?f=%28d%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csin%203x-%5Csin%20x%7D%7B%5Ccos%203x%2B%5Ccos%20x%7D%3D%5Cdfrac%7B2%5Ccos%20%5B%5Cfrac%7B3x%2Bx%7D%7B2%7D%5D%20%5Csin%20%5B%5Cfrac%7B3x-x%7D%7B2%7D%5D%7D%7B2%5Ccos%20%5B%5Cfrac%7B3x%2Bx%7D%7B2%7D%5D%5Ccos%20%5B%5Cfrac%7B3x-x%7D%7B2%7D%5D%7D%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B2%5Ccos%202x%5Csin%20x%7D%7B2%5Ccos%202x%5Ccos%20x%7D%3D%5Cdfrac%7B%5Csin%20x%7D%7B%5Ccos%20x%7D%5C%5C%5C%5C%5CRightarrow%20%5Ctan%20x)
Thus, all the identities are correct.
Answer:False
Step-by-step explanation:
A(b+c)=a*b+a*c CORRECT
2(y+11)=2*y+2*11), BUT better 11y+22 both are CORRET
Least to greatest is mB,mD,mC
<h3>
Answer: (x+1)(x+3)</h3>
===================================================
Explanation:
Let's assume it factors into (x+a)(x+b)
The goal is to find the two numbers a and b.
FOIL out (x+a)(x+b) to get x^2+(a+b)x+ab
Note how a+b is the middle term and ab is the last term.
In the original expression, 4 is the middle term and 3 is the last term.
So we need to find two numbers that
There are two ways to multiply to 3 and they are
- 1 times 3 = 3
- -1 times -3 = -3
But only the first way has the factors add to 4. So that means a = 1 and b = 3.
Therefore (x+a)(x+b) = (x+1)(x+3)
And x^2+4x+3 = (x+1)(x+3)
