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
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This is the slope formula.
Given:
The graph of a function is given.
To find:
The range of the graph.
Solution:
We know that, the domain is the set of input values and range is the set of output values.
In a graph, domain is represented by the x-axis and range is represented by the y-axis.
From the given graph it is clear that there is an open circle at (-8,-8) and a closed circle at (3,4). It means the function is not defined at (-8,-8) but defined for (3,4).
The graph of the function is defined over the interval 
. So, the domain is (-8,3].
The values of the function lie in the interval 
. So, the range is (-8,4].
Therefore, the range of the function are all real values over the interval (-8,4].
profit, p = 6 × $50 = $300
losses, l = 120 + 30 + 200 = $350
overall = p - l = -$50
loss of $50
Answer:
The sum of the interior angles of any triangle is equal to 180 degrees.
