Question

if cos B =3/5 find the value of sec^2B -1

Answer 1

$\cos(b) = \frac{3}{5} \\ we \: know \: that \\ \frac{1}{cos} = sec \\ so \: \sec(b) = \frac{5}{3}$
we have to find sec²(B) -1
so
$\frac{ {5}^{2} }{ {3}^{2} } - 1$
$\frac{25}{9} - 1 \\ = \frac{25 - 9}{9} \\ = \frac{16}{9}$

Answer 2

cosB=3/5
coB=1/secB
secB=1/cosB=5/3
sec^2B-1=(5/3)^2-1
=25/9-1/1
=(25-9)/9
=16/9