Find the exact value of trigonometric function sec2x if sinx =3/5, cosx=4/5

Since sec 2x = 1/cos 2x, we'll have to determine the value of
cos 2x, given the values of sin x and cos x.

cos 2x = cos
(x+x)

cos 2x = cos x*cos x - sin x*sin
x

cos 2x = (cos x)^2 - (sin x)^2

We'll
substitute cos x and sin x by the given values:

sinx =3/5
and cosx=4/5

cos 2x = (4/5)^2 -
(3/5)^2

cos 2x = 16/25 - 9/25

cos 2x =
7/25

We'll substitute the value of cos 2x in the formula of sec
2x:

sec 2x = 1/(7/25)

The
exact value of sec 2x = 25/7.