Question #b0c1d

1 Answer
Ratnaker Mehta
Jan 3, 2018

#=1/8*sqrt6(sqrt3-1)#.

Explanation:

I hope, the Question is, #cos45/(sec30+csc30)#

Now, we know that, #cos45=1/sqrt2, sec30=1/cos30=1/(sqrt3/2)#, and, #csc30=1/sin30=1/(1/2)#.

#:."The Reqd. Value="(1/sqrt2)/(2/sqrt3+2)=1/sqrt2{sqrt3/(2+2sqrt3)},#

#=sqrt3/{2sqrt2(sqrt3+1)}=sqrt3/{2sqrt2(sqrt3+1)}xx(sqrt3-1)/(sqrt3-1)xxsqrt2/sqrt2#,

#=1/8*sqrt6(sqrt3-1)#.

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