Math, asked by guptanaresh582, 1 year ago

Cos 45/


sec 30° + cosec 30

Answers

Answered by navu31
1

Answer:

hope so its the right answer

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Answered by Anonymous
0

\sf\large\frac{cos\:45}{sec\:30+csc\: 30}

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∵ ( cos 45 = 1/√2

sec 30 = 2/√3

csc 30 = 2 )

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by substituting the values :-

\sf\frac{\frac{1}{\sqrt{2}}}{(\frac{2}{\sqrt{3}})+(\frac{2}{1})}=  \frac{\frac{1}{\sqrt{2}}}{\frac{2+2 \sqrt{3}}{\sqrt{3}}}

(we will interchange the places of √3 and 1 so as not to get the value in negative form)

\sf\frac{1}{\sqrt{2}}\times  \frac{\sqrt{3}}{2+2\sqrt{3}}=\frac{1}{\sqrt{2}}\times\frac{\sqrt{3}}{2(\sqrt{3}+1)}

( Rationalizing the denominator because the final value must not be irrational )

\sf\frac{\sqrt{3}}{2\sqrt{2}(\sqrt{3}  + 1)}\times\frac{\sqrt{2}(\sqrt{3}-1)}{\sqrt{2}(\sqrt{3}-1)}

\sf\frac{\sqrt{6}(\sqrt{3}-1)}{4(({\sqrt{3})}^{2}-({1)}^{2}}

\sf\frac{\sqrt{18} -\sqrt{6}}{4(2)}

\sf\frac{\sqrt{2\times3\times 3}-  \sqrt{2\times3}}{8}

\sf\boxed{\frac{3\sqrt{2}-\sqrt{6}}{8}}

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