Question

Evaluate the following :

sin 30°+ tan 45°- cosec 60°/ cot 45° + cos 60° - sec 30°



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Answer 1

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$\huge\frac{sin30°+tan45°-cosec60°}{cot45°+cos60°-sec30°}$

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

$= = > \huge\frac{ \frac{3}{2} - \frac{2}{ \sqrt{3} } }{\frac{3}{2} - \frac{ 2}{ \sqrt{3} } }$

$Rationalise \: \Large \frac{ \frac{3}{2} - \frac{2}{ \sqrt{3} } }{ \frac{3}{2} - \frac{2}{ \sqrt{3} } } \\ = = >\Large \frac{ \frac{3}{2} - \frac{2}{ \sqrt{3} } }{ \frac{3}{2} - \frac{2}{ \sqrt{3} } } \times \frac{ \frac{3}{2} + \frac{2}{ \sqrt{3} } }{ \frac{3}{2} + \frac{2}{ \sqrt{3} } } \\ = = > \Large \frac{ (\frac{3}{2} )² - ( \frac{2}{ \sqrt{3} })² }{( \frac{3}{2}) ² - (\frac{2}{ \sqrt{3} }) ²} \\ = = >\Large \frac{ \frac{9}{4} - \frac{4}{3} }{ \frac{9}{4} - \frac{4}{3} } \\ \Large LCM \: of \: 3 \: and \: 4 \: is \: 12. \\ = = > \Large \frac{9}{4} \times \frac{3}{3} = \frac{27}{12} \\ = = > \Large\frac{4}{3} \times \frac{4}{4} = \frac{16}{12} \\ = = > \Large \frac{ \frac{27}{12} - \frac{16}{12} }{ \frac{27}{12} - \frac{16}{12} } \\ = = > \Large\frac{ \frac{11}{12} }{ \frac{11}{12} } \\ = = > \cancel\frac{11}{12} \times \cancel\frac{12}{11} \\ = = > \huge1$

$\Large{\textsf{\textbf{\color{yellow}{Helps\:uh\:for\:sure\:!!}}}}$

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Answer 2

hehehe theliyadhu ra

sorry