How do you find the exact value of $sin(135^circ-30^circ)$ ?

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Answer 1 · 2017-02-03T19:23:34

$sin(135-30)=(sqrt3+1)/(2sqrt2)$

$sin(a-b)=sinacosb-sinbcosa$

$sin30=1/2$

$cos30=sqrt3/2$

$sin(135-30)=sin135cos30-cos135sin30=sqrt(3)/2sin135-1/2cos135$

as $sin135=sin(180-45)=sin45=1/sqrt2$

and $cos135=cos(180-45)=-cos45=-1/sqrt2$

Hence $sin(135-30)=sqrt3/2xx1/sqrt2-1/2xx-(-1/sqrt2)=(sqrt3+1)/(2sqrt2)$

How do you find the exact value of sin(135^circ-30^circ)sin(135^circ-30^circ)?