Question

5 Соs 45
Sec 30 + cosec 30​

Answer 1

Correct question :

• $\blue{\sf\dfrac{cos45^\circ}{sec30^\circ+cosec^\circ}}$

To find :

• Its value

Solution :

$\implies \red{\sf\dfrac{ \dfrac{1}{ \sqrt{2} } }{ \dfrac{2}{ \sqrt{3} + 2 } } = \dfrac{ \dfrac{1}{ \sqrt{2} } }{ \dfrac{2 + 2 \sqrt{3} }{ \sqrt{3}} }} \\ \\ \\ \implies \purple{\sf\dfrac{1}{ \sqrt{2} } \times \dfrac{ \sqrt{3} }{2 + 2 \sqrt{3} } = \dfrac{ \sqrt{3} }{ \sqrt{2} \times 2( \sqrt{3} + 1) }} \\ \\ \\ \implies\pink{\sf\dfrac{ \sqrt{3} }{ \sqrt{2} \times 2( \sqrt{3} + 1) } \times \dfrac{ \sqrt{3} - 1 }{ \sqrt{3} - 1 }} \\ \\ \\ \implies \green{\sf \dfrac{ \sqrt{3}( \sqrt{3} - 1) }{ \sqrt{2} \times 2(3 - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \sf(since(a + b)(a - b) = (a^{2} - b^{2} ))} \\ \\ \\ \implies \orange{ \sf\dfrac{ \sqrt{3}( \sqrt{3} - 1) }{4 \sqrt{2}} \times \dfrac{ \sqrt{2} }{ \sqrt{2} }} \\ \\ \\ \implies \underline{\boxed{\gray{\sf \dfrac{3 \sqrt{2} - \sqrt{6} }{8}}}}$