Kenneth S. answered • 07/02/17

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Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018

e is a very poor choice for this problem, inasmuch as it should be reserved for the base of the natural logarithms.

If tan

^{2}θ = sec^{2}θ - 1 (Pythag. identity) = 1-e^{2}(as given). Therefore tan^{3}θ = (1-e^{2})^{3/2}.Also, sec

^{2}θ = (2 - e^{2})What, then, is csc θ ? tan θ = (sin θ) / (cos θ) so sin θ = tan θ cos θ

so csc θ = 1 / [tan θ cos θ] = sec θ / tan θ = (2-e

^{2})^{½}/ (1-e^{2})^{½}.You desire to simplify, in terms of e, this: sec

^{2}θ+ tan^{3}θ csc θ...Your task is to (1) check all of the work, so far, and then (after any necessary correction),

(2) substitute all of the appropriate e-related expressions, and simplify.

I leave this to you because it's a typing/proofreading nightmare, and besides, you need to participate.