Question

please proof it fast.

Answer 1

a/ 2(b-c) = cos^2(A/2)/ (cosC-cosB)

lhs = a / 2 (b – c )

Now use sine rule

a/ sinA = b/ sinB = c/ sinC = k

So, lhs = a / 2 (b – c )= sinA / 2(sinB -sinC)

=SinA /2* 2 cos(B+C/2) cos (B-C/2)

= sinA / 4 cos (pi/2 – A/2) cos (B-C/2)

=2 sin(A/2) cos (A/2) / 4 sin(A/2) cos (B-C/2)

= cos (A/2) / cos(B-C/2)

=cos2(A/2)/ Cos(A/2) cos(B-C/2)

= cos2(A/2)/ Cos(90 – (B+C)/2) cos(B-C/2)

=2 cos2(A/2)/ 2 sin((B+C)/2) cos(B-C/2)

= 2 cos2(A/2)/ 2 sin((B+C)/2) cos(B-C/2)

=cos2(A/2)/ (cosC-cosB)

Answer 2

$\bold \red{hello !!!}$

$"solution \: is \: in \: this \: given \: attachment"$

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$\underline \orange{Rajukumar111}$