Question

square of 9 tan 60 + 9 cos 60
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Answer 1

$\red{ Value \: of \: ( 9tan 60\degree + 9 cos 60 \degree )^{2} } \\= [ 9( tan 60 \degree + cos 60 \degree)]^{2} \\= 81\Big( \sqrt{3} + \frac{1}{2} \Big)^{2} \\= 81[ 3 + \frac{1}{2^{2}} + 2 \times \sqrt{3} \times \frac{1}{2} ]\\= 81 [ 3 + \frac{1}{4} + \sqrt{3} ]\\= 81 [ \frac{12+1+4\sqrt{3}}{4}] \\= 81 [ \frac{13+4\sqrt{3}}{4}]$

Therefore.,

$\red{ Value \: of \: ( 9tan 60\degree + 9 cos 60 \degree )^{2} } \green { = 81 [ \frac{13+4\sqrt{3}]}{4}}$

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