Question 1076620

Verify the identity.

(1/cosx+1) + (1/cosx-1) = -2cscx cot x
<pre>{{{1/(cos (x) + 1) + 1/(cos (x) - 1) = - 2 csc (x) cot (x)}}}
Left side: {{{(cos (x) - 1 + cos (x) + 1)/(cos (x) + 1)(cos (x) - 1)}}} ------ Multiplying by LCD, (x + 1)(x - 1)
            {{{(2 cos (x))/(cos^2 (x) - 1)}}}
            {{{(2 cos (x))/(1 - sin^2 (x) - 1)}}} ------- Substituting {{{matrix(1,3, 1 - sin^2 (x), for, cos^2 (x))}}}
            {{{(2 cos (x))/(- sin^2 (x))}}} =======> {{{(- 2 * cos (x))/sin^2 (x)}}} =======> {{{- 2 * (cos (x)/sin (x)) * (1/sin (x))}}} =======> {{{highlight_green(- 2 * cot (x) * csc (x))}}} (Same as RIGHT side so this has been proven)