Question

Prove that (a) (1+siny)/(1-siny)=(1-siny)/(1+siny)=(4tany)/(cosy) fol Which values of y in the intarval 360;360 is 7 e indemed

Answer 1

To prove the equality, multiply the numerator and denominator by (1+siny), simplify, and conclude that it holds true for any value of y except when cosy=0.

Step-by-step explanation:

To prove that (a) (1+siny)/(1-siny)=(1-siny)/(1+siny)=(4tany)/(cosy), we can start by multiplying the numerator and denominator of the left side of the equation by (1+siny). This gives us:

(1+siny)/(1-siny) * (1+siny)/(1+siny) = (1+siny)(1+siny) / (1-siny)(1+siny)

Simplifying both the numerator and denominator, we get:

(1 + 2siny + sin^2y) / (1 - sin^2y) = (cos^2y + 2cosy + 1) / (cos^2y - sin^2y) = cos^2y / cosy = 4tany / cosy

Therefore, we have proven the equality for any value of y, except when cosy=0.