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:
no trangles can be formed
Step-by-step explanation:
We have been given angle A as 75 degrees and sides a = 2 and b = 3.
Using Sine rule, we can set up:
sin(a) sin(b)
------------ = ------------
A B
Upon substituting the given values of angle A, and sides a and b, we get:
sin(75) sin(B)
------------ = ------------
2 3
Upon solving this equation for B, we get:
----->3sin(75)=2sin(B)
----->sin(B)=3sin(75)
-------------
2
------>sinB=1.4488
Since we know that value of Sine cannot be more than 1. Hence there are no values possible for B.
Hence, the triangle is not possible. Therefore, first choice is correct.
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Answer: I believe it is D..
