if a b and c are the interior angles of triangle ABC show that 1) cos a+ b/ 2 = sin C / 2
2) tan c+a/2=cot b/2
please and it fast unwanted and would be reported and the right and would be marked as brain lest
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Step-by-step explanation:
Considering that angle C = 90°
so by angle sum property
angle A + angle B =180-Angle C
which will give angle a+b = 90
now ,
cos a+b/2= cos 90/2=cos 45 =1/√2
and
sin c/2= sin 90/2=sin 45=1/√2
which means cos a+b/2= sin c/2
Now considering angle b = 90°
by ASP,
angle a+c=180-b
a+c=90
so, tan a+c/2=tan 90/2=tan 45=1
and
cot b/2=cot 90/2=cot 45=1
so,
tan a+c/2=cot b/2
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