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

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We are given that sin x = 1/4 and cos x = 3/4. We have to find sec 2x.

sec 2x = 1/ cos 2x

cos 2x = (cos x)^2 - (sin x)^2

=> (3/4)^2 - (1/4)^2

=> (9 - 1)/ 16

=> 8/ 16

=> 1/2

So **sec 2x = 2**

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.**