Question 1054131
Let tan(theta)=3 with theta om Quadrant I and find the following.
sec2(theta)

This is what I have done
found tan(theta)=3/1 cos(theta)=sqrt10/10 sin(theta)=3*sqrt10/10
from what I was taught I use the double angle formula cos2(theta)=cos^2(theta)-sin^2(theta), plug in your cos and sin and then sec2(theta) would be 1/cos2(theta)
I keep trying to find the  cos2(theta) value but keep coming up with the wrong answer after plugging it in to sec2(theta) (checked in the back of my book)
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tan(theta)=3
tan = y/x =  3/1
r = sqrt(3^2 + 1^2) = sqrt(10)
---
cos(t) = x/r = 1/sqrt(10)
cos(2t) = 2cos^2(t) - 1 = (1/5) - 1 = -4/5
sec(2t) = -5/4
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Using the sine as you did:
tan(theta)=3
tan = y/x =  3/1
r = sqrt(3^2 + 1^2) = sqrt(10)
sin(t) = y/r = 3sqrt(10)/10
---
cos(2t) = cos^2(t) - sin^2(t) = (1/10) - 9/10 = -4/5
sec(2t) = -5/4