Answer:
D
Step-by-step explanation:
B and C aren't correct
Angle a,b,c equals 222; because angle a and b already is 180; so there is a right angle in the top with a 48 degree next to it so add then up and its 138; now subtract 180 which is the total of the total angels with 138 and you get 42; now add that to 180 and you get your answer which is 222.
I'll solve for y
xy+(4(20))>x-5y(2+9-7)
xy+4(20)>x-5y(2+9-7)
xy+4(20)>x-5y(4)
xy+4(20)>x-20y
xy+80>x-20y
xy+20y+80>x
y(x+20)>-80+x
y>(-80+x)/(x+20)
Remember: We have to work from either the LHS or the RHS.
(Left hand side or the Right hand side)
You should already know this:
1.
![\boxed{\bf{\huge{tan \theta = \frac{sin \theta}{cos \theta}}}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbf%7B%5Chuge%7Btan%20%5Ctheta%20%3D%20%5Cfrac%7Bsin%20%5Ctheta%7D%7Bcos%20%5Ctheta%7D%7D%7D%7D%3Cspan%3E)
2.
![\boxed{\bf{\huge{cot\theta =\frac{1}{tan\theta}}}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbf%7B%5Chuge%7Bcot%5Ctheta%20%3D%5Cfrac%7B1%7D%7Btan%5Ctheta%7D%7D%7D%7D)
3.
![\boxed{\bf{\huge{sin^2\theta +cos^2 \theta = 1}}}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbf%7B%5Chuge%7Bsin%5E2%5Ctheta%20%2Bcos%5E2%20%5Ctheta%20%3D%201%7D%7D%7D%7D)
<span>So, our question is:
</span>
![\sf{\huge{tan\theta + cot\theta=\frac{1}{sin\theta cos\theta}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Chuge%7Btan%5Ctheta%20%2B%20cot%5Ctheta%3D%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%7D%7D)
Plug in the first two identities I gave you.
![\sf{\frac{sin\theta}{cos\theta} +\frac{1}{tan\theta} =\frac{1}{sin\theta cos\theta}](https://tex.z-dn.net/?f=%5Csf%7B%5Cfrac%7Bsin%5Ctheta%7D%7Bcos%5Ctheta%7D%20%2B%5Cfrac%7B1%7D%7Btan%5Ctheta%7D%20%3D%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D)
Apply the first identity I said you needed to know on 1/(tan θ). We should get:
![\sf{\frac{sin\theta}{cos\theta} +\frac{1}{\frac{sin\theta}{cos\theta}} =\frac{1}{sin\theta cos\theta}}\\\\\\\sf{\frac{sin\theta}{cos\theta} +\frac{cos\theta}{sin\theta} =\frac{1}{sin\theta cos\theta}](https://tex.z-dn.net/?f=%5Csf%7B%5Cfrac%7Bsin%5Ctheta%7D%7Bcos%5Ctheta%7D%20%2B%5Cfrac%7B1%7D%7B%5Cfrac%7Bsin%5Ctheta%7D%7Bcos%5Ctheta%7D%7D%20%3D%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%7D%5C%5C%5C%5C%5C%5C%5Csf%7B%5Cfrac%7Bsin%5Ctheta%7D%7Bcos%5Ctheta%7D%20%2B%5Cfrac%7Bcos%5Ctheta%7D%7Bsin%5Ctheta%7D%20%3D%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D)
Multiply the first fraction by sinθ, on both the numerator and denominator.
Multiply the second fraction by cos<span>θ, on both the numerator and denominator.
</span>
![\sf{\frac{sin\theta \times sin\theta}{cos\theta \times sin\theta} +\frac{cos\theta \times cos\theta}{sin\theta \times cos\theta} =\frac{1}{sin\theta cos\theta}}\\\\\\ \sf{\frac{sin^2\theta}{sin\theta cos\theta} + \frac{cos^2 \theta}{sin\theta cos\theta} = \frac{1}{sin\theta cos\theta}}\\\\\\\sf\frac{sin^2\theta + cos^2\theta}{sin\theta cos\theta} =\frac{1}{sin\theta cos\theta}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cfrac%7Bsin%5Ctheta%20%5Ctimes%20sin%5Ctheta%7D%7Bcos%5Ctheta%20%5Ctimes%20sin%5Ctheta%7D%20%2B%5Cfrac%7Bcos%5Ctheta%20%5Ctimes%20cos%5Ctheta%7D%7Bsin%5Ctheta%20%5Ctimes%20cos%5Ctheta%7D%20%3D%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%7D%5C%5C%5C%5C%5C%5C%20%5Csf%7B%5Cfrac%7Bsin%5E2%5Ctheta%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%20%2B%20%5Cfrac%7Bcos%5E2%20%5Ctheta%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%20%3D%20%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%7D%5C%5C%5C%5C%5C%5C%5Csf%5Cfrac%7Bsin%5E2%5Ctheta%20%2B%20cos%5E2%5Ctheta%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%20%3D%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%7D)
Now, use the third identity I said that you needed to know to simplify the numerator.
![\sf{\frac{sin^2\theta +cos^2\theta}{sin\theta cos\theta} =\frac{1}{sin\theta cos\theta}}\\\\\\\sf{\frac{1}{sin\theta cos\theta}=\frac{1}{sin\theta cos\theta}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cfrac%7Bsin%5E2%5Ctheta%20%2Bcos%5E2%5Ctheta%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%20%3D%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%7D%5C%5C%5C%5C%5C%5C%5Csf%7B%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%3D%5Cfrac%7B1%7D%7Bsin%5Ctheta%20cos%5Ctheta%7D%7D)
LHS = RHS
<span>
Therefore, identity is verified.</span>
Answer:
The answers is K = 24 and J + 12