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1. Homework Statement

1. Homework Statement

Show the following: $$ \frac { 3 cos^2(x) } { 2 - 2 sin(x) } = \frac { 3 }{ 2 } ( sin(x) + 1 ) $$

## Homework Equations

$$ sin^2(x) + cos^2(x) = 1 $$ $$ cos^2(x) = 1 - sin^2(x) $$

## The Attempt at a Solution

I make it about halfway to a solution and then draw a blank.

$$ \frac { 3 cos^2(x) } { 2 - 2 sin(x) } = \frac { 3 (1 - sin^2(x)) } { 2 - 2 sin(x) } $$ $$ = \frac { 3 - 3 sin^2(x) } { 2 - 2 sin(x) } $$ I get the feeling I've overlooked something fairly obvious or swapped a sign somewhere, but it's not jumping off the page at me. Any nudges in the right direction are greatly appreciated.