Question #58dad

1 Answer
Nov 19, 2017

sin(A/2)=sqrt((65-sqrt(65))/130)

Explanation:

Here, secA=sqrt(65)

or, cosA=1/sqrt(65)

We have, sin(A/2)=+-sqrt((1-cosA)/2

Taking +sign only as A is acute angle.

Then sin(A/2)=sqrt((1-1/sqrt(65))/2

sin(A/2)=sqrt(((sqrt(65)-1)/sqrt(65))/2)

=sqrt((sqrt(65)-1)/(2*sqrt(65))

=sqrt((sqrt(65)-1)/(2*sqrt(65))*(sqrt65)/sqrt(65))

=sqrt((65-sqrt(65))/130)