Tanθ + cotθ = 1/sinθcos<span>θ
since we know that;
tan</span>θ = sinθ/cos<span>θ, and
cot</span>θ = cosθ/sin<span>θ
now when we add tan</span>θ and cot<span>θ and replace their values;
tan</span>θ + cot<span>θ=sin</span>θ/cosθ + cosθ/sin<span>θ
</span>For a common denominator to add those two fractions, the obvious choice is sinθ.cosθ , so
tanθ + cotθ = sin²θ/sinθcosθ + cos²θ/sinθcosθ =sin²θ + cos²θ / sinθcosθ
now we can use the identity that;
sin²θ + cos²θ = 1
So,
tanθ + cotθ = 1/sinθcosθ
Answer:
x = 1.27
y = 5.18
Step-by-step explanation:
to solve this system of equation by simultaneous equation we say that let
3x+y=9.............................. equation 1
-5x+2y=4 .......................... equation 2
from equation 1
3x+y=9.............................. equation 1
y = 9 -3x.............................. equation 3
substitute the value of y = 9 -3x into equation 2
-5x+2y=4 .......................... equation 2
-5x + 2( 9 -3x) = 4
-5x + 18 - 6x = 4
collect the like terms
18 - 4 = 6x + 5x
14 = 11x
divide both side by 11
14/11 = 11x/11
x = 14/11
x = 1.27
put the value of x = 1.27 into equation 3
y = 9 -3x.............................. equation 3
y = 9 - 3( 1.27)
y = 9 - 3.82
y = 5.18
<em>to check if you are correct put the value of x and y into either equation 1 or equation 2.</em>
<em>3x+y=9.............................. equation 1</em>
<em>3( 1.27) + 5.18 = 9</em>
<em>3.81 + 5.18 = 9</em>
<em>9 = 9</em>
Answer:
sold 120 chocolate bars
sold 140 peanut butter bars
Step-by-step explanation:
x = peanut butter bars
y = chocolate bars
x + y = 260, total lbs
0.25x + 0.30y = 71, money
solve double variable equation
multiply -4 on both sides for 2nd equation
-x + -1.2y = -284
add both equations together
-0.2y = -24
y = 120
x = 260 - 120
x = 140
sold 120 chocolate bars
sold 140 peanut butter bars
<span>7x+6y=30
6y = -7x + 30
y = -7/6x + 5
answer:
slope = -7/6</span>
Answer:
Plug x-7 in for y, in the bottom equation.
x - 7 = 2 + 2x - 4
x - 7 = 2x - 2
x = 2x + 5
-x = 5
x = -5
