(a) $\tan \dfrac{\pi }{9}-\dfrac{\sin \dfrac{\pi }{9}}{\cos \dfrac{\pi }{9}}\underset{\underset{\color{#0066A7}{\hbox{\(\dfrac{\sin \theta }{\cos \theta }{=}\tan {\theta }\)}}}{\color{#0066A7}{\displaystyle\uparrow }}}{=} \tan \dfrac{\pi }{9}-\tan \dfrac{\pi }{9}=0$

(b) $\sin ^{2}\dfrac{\pi }{12}+\dfrac{1}{\sec ^{2}\dfrac{\pi }{12}}\underset{\underset{\color{#0066A7}{\hbox{\(\cos { \theta =}\frac{1}{\sec \theta}\)}}}{\color{#0066A7}{\uparrow}}}{=} \sin ^{2}\dfrac{\pi }{12}+\cos ^{2}\dfrac{\pi }{12}\underset{\underset{\color{#0066A7}{\hbox{\(\sin ^{2}{ \theta +}\cos ^{2}{ \theta =1}\)}}}{\color{#0066A7}{\uparrow}}}{=}1$