Question

sin30+tan45-cosec60by cot45+cos60-sec60​

Answer 1

$\bf \huge \underline \purple{Answer : }$

$\sf \implies \: \frac{sin \: 30 + tan \: 45 - \: cosec \: 60}{cot \: 45 + cos \: 60 - sec \: 60}$

$\sf \implies \: \frac{ \frac{1}{2} + 1 - \frac{2}{ \sqrt{3} } }{ \frac{2}{ \sqrt{3} } + \frac{1}{2} + 1 }$

$\sf \implies \: \frac{ \sqrt{3} + 2 \sqrt{3} - 4 }{4 + \sqrt{3} + 2 \sqrt{3} }$

$\sf \implies \: \frac{3 \sqrt{3} - 4 }{4 + 3 \sqrt{3} }$

Rationalising the denominator,

$\sf \implies \: \frac{3 \sqrt{3} - 4}{4 + 3 \sqrt{3} } \times \frac{3 \sqrt{3} - 4}{3 \sqrt{3} - 4 }$

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

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

$\sf \implies \: \frac{43 - 24 \sqrt{3} }{11}$

Answer 2

Step-by-step explanation:

Rationalising the denominator,

\begin{gathered}\sf \implies \: \frac{3 \sqrt{3} - 4}{4 + 3 \sqrt{3} } \times \frac{3 \sqrt{3} - 4}{3 \sqrt{3} - 4 } \\\end{gathered}

⟹

4+3

3

3

3

−4

×

3

3

−4

3

3

−4

\begin{gathered}\sf \implies \: \frac{ {(3 \sqrt{3} - 4})^{2} }{ {(3 \sqrt{3} })^{2} - {(4)}^{2} } \\\end{gathered}

⟹

(3

3

)

2

−(4)

2

(3

3

−4)

2

\begin{gathered}\sf \implies \: \frac{27 + 16 - 24 \sqrt{3} }{27 - 16} \\\end{gathered}

⟹

27−16

27+16−24

3

\begin{gathered}\sf \implies \: \frac{43 - 24 \sqrt{3} }{11} \\\end{gathered}

⟹

11

43−24

3