26. If A=cosB +sinB ,then for all values of B, prove that 3/4 <=A<=1

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If $c o s A + c o s B = \frac{1}{2}$ and $s i n A + s i n B = \frac{1}{4}$ , prove that: $t a n (\frac{A + B}{2}) = \frac{1}{2}$

cos A + cos B = \frac{1}{2}

sin A + sin B = \frac{1}{4}

\frac{tan (A + B)}{2} = \frac{1}{2}

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