Please solve and provide a step by step hand written solution for part d 4. For each equation, either prove that it is an identity or give a counterexample that provesit is not. Describe the process you followed.a. tan(a + b) = tan(a) + tan (b)b. tan(x + 7) = tan(x)c. - cos(2x) = sin(x) − cos4 (x)d. cot(x) csc(x):=sin(x) cos(x)-sin(x)sin²(x)

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Answered: d. cot(x) - csc(x) = sin(x)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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After answering Part 1 and 2, What do you find as the solution?
An ecologist is studying the impacts of air pollution on giant panda populations, specifically on panda birth rates. Due to the historical interest in giant pandas, the ecologist has access to data from the last 30 years that allows her to fit two models to the evolution of giant panda populations over time (one for 30 years and one for the last 5 years after a new chemical plant was built close to the panda habitat). She will use these models to determine the long-term impacts of this pollution on panda populations. She has the following information to help her model the two sets of population dynamics data on adult and baby pandas : i. 1) Without pollution, for every 1 adult female panda a year earlier, 0.75 baby pandas are born each year (reproduction rate = 0.75). 2) With pollution, for every 1 adult female panda a year earlier, 0.7 baby pandas are born each year (reproduction rate = 0.7). 3) 3 in 4 of the adult female pandas survive to the next year. 1 in 3 female baby pandas…
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d. cot(x) - csc(x) = sin(x) cos(x)-sin(x) sin²(x)