Answer
(a) $sin(135°-30°)=\frac{\sqrt 6-\sqrt 2}{4}$
(b) $sin~135°-cos~30°=-\frac{\sqrt 3-\sqrt 2}{2}$
Work Step by Step
(a) $sin(135°-30°)=sin~135°cos~~30°-cos~135°sin~30°=\frac{\sqrt 2}{2}\frac{\sqrt 3}{2}-(\frac{\sqrt 2}{2})\frac{1}{2}=\frac{\sqrt 6}{4}-\frac{\sqrt 2}{4}=\frac{\sqrt 6-\sqrt 2}{4}$
(b) $sin~135°-cos~30°=\frac{\sqrt 2}{2}-\frac{\sqrt 3}{2}=\frac{\sqrt 2-\sqrt 3}{2}=-\frac{\sqrt 3-\sqrt 2}{2}$
