Answer:
2
Explanation:
To find the value of tan(theta) + sec(theta) when sin(theta) is equal to 6/10, we can use trigonometric identities.
First, let's find cos(theta) using the Pythagorean identity:
sin^2(theta) + cos^2(theta) = 1
Given that sin(theta) = 6/10, we can find cos(theta):
(6/10)^2 + cos^2(theta) = 1
36/100 + cos^2(theta) = 1
cos^2(theta) = 1 - 36/100
cos^2(theta) = 64/100
cos(theta) = ±8/10
Since cosine is positive in the first and fourth quadrants, we'll take the positive value:
cos(theta) = 8/10 = 4/5
Now, we can find tan(theta) and sec(theta):
tan(theta) = sin(theta) / cos(theta) = (6/10) / (4/5) = (6/10) * (5/4) = 30/40 = 3/4
sec(theta) = 1 / cos(theta) = 1 / (4/5) = 5/4
Finally, we can calculate tan(theta) + sec(theta):
tan(theta) + sec(theta) = (3/4) + (5/4) = 8/4 = 2
So, the value of tan(theta) + sec(theta) when sin(theta) is equal to 6/10 is 2.