Given sinx=1/4 and cosx=3/4 what is sec2x ?

Since the formula for sec 2x = 1/cos 2x, we'll have
to find out 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 =1/4
and cosx=3/4

cos 2x = (3/4)^2 -
(1/4)^2

cos 2x = (3/4 - 1/4)(3/4 +
1/4)

cos 2x = 2/4

cos 2x =
1/2

2x = pi/3 + 2k*pi

x =
pi/6 + 2k*pi

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

sec 2x =
1/(1/2)

The exact value of sec 2x =
2.