SOLUTION: If sin 𝛼 + sin 𝛽 = 𝑝, cos 𝛼 − cos 𝛽 = 𝑞, where 𝑝 ≠ 0 and 𝑝 ≠ 𝑞, find cot(𝛼 − 𝛽) in terms of 𝑝 and 𝑞.

Question 1204327: If sin 𝛼 + sin 𝛽 = 𝑝, cos 𝛼 − cos 𝛽 = 𝑞, where 𝑝 ≠ 0 and 𝑝 ≠ 𝑞, find cot(𝛼 − 𝛽) in terms of 𝑝 and 𝑞.
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!
If sin 𝛼 + sin 𝛽 = 𝑝, cos 𝛼 − cos 𝛽 = 𝑞, where 𝑝 ≠ 0 and 𝑝 ≠ 𝑞,
find cot(𝛼 − 𝛽) in terms of 𝑝 and 𝑞.

We use the sum/difference to product trig identities: We use the trig identity with Multiply top and bottom by q²: Edwin

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answered previously at this link
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204374.html

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