Question

sin30⁰-sin90⁰+2cos0⁰/tan30⁰ tan60⁰

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Answer 1

$\bold \color{green} { \underline{ \underline { \green \mid\red {\mid{required \: answer}}} \red \mid \mid}}$

we have,

$\bold { \frac{ { \sin }^{2} 45 \degree + { \cos}^{2} 45 \degree}{ {tan}^{2}60 \degree } }$

$\bold{ \implies \frac{{( \sin45 \degree) }^{2} + {( \cos45 \degree) }^{2} }{ {( \tan60 \degree)}^{2} } }$

$\bold{ \implies \frac{ ({ \frac{1}{ \sqrt{2} } )}^{2} + ({ \frac{1}{ \sqrt{2} } )}^{2} }{ { (\sqrt{3} }^{2}) } }$

$\bold{\implies \frac{ \frac{1}{2} + \frac{1}{2} }{3}}$

$\huge \bold{\implies \frac{1}{3} }$

$hence.. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \frac{1}{3} \: is \: \:the \: \: right \ \: answer..$