In triangle ABC, show that sin square A/2 + sin square B+C/2=1
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Step-by-step explanation:
A+B+C= 180
A= 180-(B+C)
on dividing both side by 2
A/2= {180-(B+C)}/2
A/2= 90-(B+C)/2
on multiply both side by sin²
sin²A/2= sin²{90-(B+C)/2}
sin²A/2= cos²(B+C)/2
sin²A/2= 1-sin²(B+C)/2
sin²A/2+sin²(B+C)/2= 1
Hence LHS=RHS proved.
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