hey how to you solve this problem:

find exact value of cosec(5pi/12):
this is what I did

= 1 / sin( pi/4 + pi/6 )
= 1 / ( sin( pi/4)cos( pi/6 ) + cos( pi/4 )sin( pi/6) )
= 1 / ( (√3/(2√2) )+( (1/(2√2)) )
= 1 / ( (√3+1) / 2√2)

then rationalised and got end answer as 4 / (√6 + √2)

but the answer in the book come as just √6 + √2

Help would be kindly appreciated.

You are correct. csc(\frac{5\pi}{12})=\sqrt{2}(\sqrt{3}-1)=\frac{4}{\sqrt{6}+\sqrt{2}}

If the book has \sqrt{6}+\sqrt{2}, then that is incorrect.

I actually get √6 - √2 when I do it. If you rationalize your denominator in
4 / (√6 + √2) you'll see it.

Strange, I'm getting \sqrt6 - \sqrt2... :confused:

From \frac{1}{\frac{\sqrt3 + 1}{2\sqrt2}}=\frac{2\sqrt2}{\sqrt3 + 1} = \frac{2\sqrt2(\sqrt3 - 1)}{(\sqrt3 + 1)(\sqrt3 - 1)} = \frac{2\sqrt2(\sqrt3 - 1)}{3-1} = \sqrt6 - \sqrt2

I actually get √6 - √2 when I do it. If you rationalize your denominator in
4 / (√6 + √2) you'll see it.

Lol, a minute difference! :p

Those LaTeX codes sure take some time.