Question

if I assume that
cos(x)+5sin(x)=23/5
and
2cos(x)+sin(x)=10/5
how would I find the exact numeric value of sec(x) and tan(x)?

Answer 1

Can you solve this system?

x + 5y = 23
2x + y = 10

Answer 2

yeah is a system of equations

Answer 3

Excellent. Apply the same principles.

cos(x)+5sin(x)=23/5
and
2cos(x)+sin(x)=10/5

From the first, cos(x) = 23/5 - 5sin(x)
Substitute into the second.

2[23/5 - 5sin(x)]+sin(x)=10/5

This leads to an exact value for sin(x) and you're almost done.