if tan square theta=1-e square,then prove that sec square+tan cube theta cosec theta=(2-e square)3/2

Question

pls answer this  question now....

Answer 1

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

 

If tan²θ = sec²θ - 1 (Pythag. identity) = 1-e² (as given).  Therefore tan³θ = (1-e²)^3/2.

Also, sec²θ = (2 - e²)

 

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-e²)^½ / (1-e²)^½.

 

You desire to simplify, in terms of e, this: sec²θ+ tan³θ 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.