We have proven that the trigonometric identity [(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] equals 1 + (secθ * cosec θ)
<h3>How to solve Trigonometric Identities?</h3>
We want to prove the trigonometric identity;
[(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] = 1 + sec θ
The left hand side can be expressed as;
[(tan θ)/(1 - (1/tan θ)] + [(1/tan θ)/(1 - tan θ)]
⇒ [tan²θ/(tanθ - 1)] - [1/(tan θ(tanθ - 1)]
Taking the LCM and multiplying gives;
(tan³θ - 1)/(tanθ(tanθ - 1))
This can also be expressed as;
(tan³θ - 1³)/(tanθ(tanθ - 1))
By expansion of algebra this gives;
[(tanθ - 1)(tan²θ + tanθ.1 + 1²)]/[tanθ(tanθ(tanθ - 1))]
Solving Further gives;
(sec²θ + tanθ)/tanθ
⇒ sec²θ * cotθ + 1
⇒ (1/cos²θ * cos θ/sin θ) + 1
⇒ (1/cos θ * 1/sin θ) + 1
⇒ 1 + (secθ * cosec θ)
Read more about Trigonometric Identities at; brainly.com/question/7331447
#SPJ1
Answer:
The answer to your question is (x + 3)² + (y + 6)² = 2
Step-by-step explanation:
Endpoints (-4, -7) and (-2, -5)
Process
1.- Find the length of the radius
d = 
d = 
d = 
d = 
d = 
Radius = 
= 
2.- Find the center
Xm = 
Ym = 
Center = (-3, -6)
3.- Write the equation
(x - h)² + (y - k)² = r²
(x + 3)² + (y + 6)² = ()²
(x + 3)² + (y + 6)² = 2
the correct answer on edge is;
a. she divided by 3 instead of the GCF.
d. she didn’t complete step 4 and use the distributive property to be sure the expressions are equivalent.
e. she didn’t undistribute the GCF from the original expression.
welcome!
Answer:
no
Step-by-step explanation:
y=mx+b
hope this helps
Based on the calculations, the amount of money she invested is equal to $3,520.
<h3>How to determine the amount invested?</h3>
First of all, we would assign variables to the amount of money that he invested at different interest rates as follows:
- Let x be the amount of money she invested at 11%.
- Let y be the amount of money she invested at 14%.
Since Lydia invested the same amount of money in both stocks, we have:
x = y ....equation 1.
At the two interest rates, the total amount Lydia gets is given by:
0.11x + 0.14y = 440 ....equation 2.
Solving the equations simultaneously, we have:
0.11y + 0.14y = 440
0.25y = 440
y = 440/0.25
y = $1,760.
Thus, the total investment is given by:
Total investment = 1760 + 1760
Total investment = $3,520.
Read more on interest rates here: brainly.com/question/16793428
#SPJ1
