Question

please answer me only any one question solve​

Answer 1

★QUESTION:-

$\frac{sin30 \degree \: + tan45 \degree - cosec60 \degree}{sec30 \degree + cos60 \degree + cot45 \degree}$

${\boxed{\underline{\tt{ \orange{Required \: \: answer \: \: is \: \: as \: \: follows:-}}}}}$

★WE KNOW:-

• Sin 30° = 1/2

• Tan 45° = 1

• Cosec 60° = 2/√3

• Sec 30° = 2/✓3

• Cos 60° = 1/2

• Cot 45° = 1

NOW, PUTTING THE VALUES IN:-

$: \implies \sf{ \frac{sin30 \degree \: + tan45 \degree - cosec60 \degree}{sec30 \degree + cos60 \degree + cot45 \degree} }$

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

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

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

Rationalising

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

(a + b) (a - b) = a^2 - b^2

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

(a - b)^2 = a^2 + b^2 -2ab

$: \implies \sf \large{ } \frac{ {(3 \sqrt{3}) }^{2} + {(4)}^{2} - 2 \times 3 \sqrt{3} \times 4 }{27 - 16}$

$: \implies \sf \large{ \frac{27 + 16 - 24 \sqrt{3} }{11} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \boxed{ \underline{ \purple{ \large{ \frac{43 - 24 \sqrt{ 3} }{11}}}}}}$