Answer:
tanx + cotx = ![\frac{1}{sinxcosx}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bsinxcosx%7D)
Step-by-step explanation:
<u><em>Explanation</em></u>
Take R.H.S = ![\frac{1}{sinxcosx}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bsinxcosx%7D)
= ![\frac{sin^{2}x+cos^{2}x }{sinxcosx}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5E%7B2%7Dx%2Bcos%5E%7B2%7Dx%20%20%7D%7Bsinxcosx%7D)
= ![\frac{sin^{2}x }{sinx cosx} + \frac{cos^{2} x}{sinxcosx}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5E%7B2%7Dx%20%7D%7Bsinx%20cosx%7D%20%2B%20%5Cfrac%7Bcos%5E%7B2%7D%20x%7D%7Bsinxcosx%7D)
= ![\frac{sinx}{cosx} + \frac{cosx}{sinx}](https://tex.z-dn.net/?f=%5Cfrac%7Bsinx%7D%7Bcosx%7D%20%2B%20%5Cfrac%7Bcosx%7D%7Bsinx%7D)
= tanx + cotx
tanx + cotx = ![\frac{1}{sinxcosx}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bsinxcosx%7D)
Answer:
Given System of equation:
x-y =6 .....,[1]
2x-3z = 16 ......[2]
2y+z = 4 .......[3]
Rewrite the equation [1] as
y = x - 6 .......[4]
Substitute the value of [4] in [3], we get
![2(x-6)+z = 4](https://tex.z-dn.net/?f=2%28x-6%29%2Bz%20%3D%204)
Using distributive property on LHS ( i.e,
)
then, we have
2x - 12 +z =4
Add 12 to both sides of an equation:
2x-12+z+12=4+12
Simplify:
2x +z = 16 .......[5]
On substituting equation [2] in [5] we get;
2x+z=2x -3z
or
z = -3z
Add 3z both sides of an equation:
z+3z = -3z+3z
4z = 0
Simplify:
z = 0
Substitute the value of z = 0 in [2] to solve for x;
![2x-3(0) = 16](https://tex.z-dn.net/?f=2x-3%280%29%20%3D%2016)
or
2x = 16
Divide by 2 both sides of an equation:
![\frac{2x}{2} =\frac{16}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%20%3D%5Cfrac%7B16%7D%7B2%7D)
Simplify:
x= 8
Substitute the value of x =8 in equation [4] to solve for y;
y = 8-6 = 2
or
y = 2
Therefore, the solution for the given system of equation is; x = 8 , y = 2 and z =0
Answer:
$5,875
Step-by-step explanation:
Interest = Principal x Time x Interest Rate
Interest = $5000 x 3.5 x 0.05
Interest = $875
Total Balance will be
$5000 + $875
= $5,875
in 3.5 years