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:
k=-7
Step-by-step explanation:
2k-6-7+3k=-48
Combine like terms
5k -13 = -48
Add 13 to each side
5k-13+13 = -48+13
5k = -35
Divide by 5
5k/5 = -35/5
k =-7
Answer:
1
Step-by-step explanation:
We can see that 7 is equal to 6, as opposite angles are the same.
We can also see that 2 is also 6, as corresponding angles are equivalent.
Therefore, 3 is also congruent to 6, as it is equal to 2.
Hope that this helps!
Answer:
A. True
Step-by-step explanation:
