Because A+B+C=180 90-A/2 =(B+C)/2
For the sake of convenience ,we get:
X=(B+C)/2 Y=A/2
SosinX=cosYand cosX=sinY
sinA=cosB-cosC
2cosXcosY=-2sinXsin((B-C)/2)
2cosXsinX=-2sinXsin((B-C)/2)
cosX+sin((B-C)/2)=0
sinY+sin((B-C)/2)=0
2sin((A+B-C)/2)cos((A-B+C)/2)=0
we get cos((A-B+C)/2)=0
(A-B+C)/2=90
A-B+C=180 (reject)
or
sin((A+B-C)/2)=0
(A+B-C)/2=0
A+B=C
so the angle C is 90
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