Question

evaluate;
(sin30 + tan45 - cosec60) / (sec30 + cos60 + cot45) {ans (43 - 24root3) / 11}

Answer 1

[tex]\frac{ \frac{1}{2} + 1 - \frac{2}{\sqrt{3}}} {\frac{2}{\sqrt{3}} + \frac{1}{2} + 1 } } \\ \\ Multiply\ numerator\ and\ denominator\ by\ 2\sqrt{3} \\ \\ \frac{3\sqrt{3} - 4}{4 +3\sqrt{3} } \\ \\ Rationalize denominator by 3 \sqrt{3} -4 \\ \\ \frac{27- 24\sqrt{3} + 16}{27-16} \\ \\ Hence\ the\ answer \\ [/tex]

Answer 2

given that
$\frac{(sin30 + tan45 - cosec60)}{(sec30 + cos60 + cot45)}$

$\frac{ \frac{1}{2}+1- \frac{2}{ \sqrt{3}} }{ \frac{2}{ \sqrt{3}}+ \frac{1}{2}+1}$

$\frac{ \sqrt{3}+2 \sqrt{3} - 4 }{4 + \sqrt{3} + 2 \sqrt{3} }$

$\frac{ 3 \sqrt{3} - 4 }{4 + 3 \sqrt{3} }$

Rationalise the denominator

$\frac{ 3 \sqrt{3} - 4 }{4 + 3 \sqrt{3} } * \frac{ 3 \sqrt{3} - 4 }{3 \sqrt{3} - 4 }$

$\frac{(3 \sqrt{3} - 4 )^2}{ (3 \sqrt{3} )^2-(4)^2 }$

$\frac{27+16-24 \sqrt{3} }{27-16}$

$\frac{43-24 \sqrt{3} }{11}$