1. You are required to verify the identity \( \frac { \tan u } { 1 + \tan ^ { 2 } u } = \sin u \cos u . \) Note that \( 1 + \tan ^ { 2 } u = \sec ^ { 2 } u \) . (This is one of the identities derived from the Pythagorean identity \( \sin ^ { 2 } u + \cos ^ { 2 } u = 1 . \)) Therefore start off as 

\( L H S = \frac { \tan u } { 1 + \tan ^ { 2 } u } = \frac { \tan u } { \sec ^ { 2 } u }\) 

then complete the verification. 

2. You are given that \( u \) is an angle in quadrant II with \( \sin u = \frac { 5 } { 6 } \) and \( w \) is an angle in the fourth quadrant with \( \cos u = \frac { 1 } { 6 } \) . 

(a) Draw \( u \) and \( w \) on the axes below then draw a right-angled triangle for \( u \) and a right-angled triangle for \( w \) .