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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Answer:
C
Step-by-step explanation:
I took the test
Answer:
4 lb
Step-by-step explanation:
10+14+40=64 oz = 4lb
Answer:
110 pages
Step-by-step explanation:
Day 1 =x
Day 2 =2x
Day 3 =x-6
(x)+(2x)+(x-6)=458
Add likes together.
4x-6=458
4x=464. Divide both sides by 4 to get x. X=116
Day 3=116-6=110
8+4p+2q+r=0
27+9p+3q+r=0
64+16p+4q+r=0
P=-9
Q=26
R=-24
