Prove that

(i)

(ii)

(iii)

(i) cos15⁰

Sin15⁰

Cos15⁰ - sin15⁰

(ii)cot105° - tan105° = cot(180° - 75°) - tan(180° - 75°)

(II quadrant tanx is negative and cotx as well)

= - cot75° - ( - tan75°)

= tan75° - cot75°

Tan75° =

(using sin(90° - x) = - cosx and cos(90° - x) = sinx)

Cot75° =

Cot105° - tan105° =

(iii)

(II quadrant tanx negative)

- tan45° = - 1