Question

Question #37b3d

Answer 1

`+- pi/3 + 2kpi`

Explanation:

Simplify both sides by `cos^2 t`. (Condition cos x different to 0)
The remainder equation is:
`1/(cos^2 t) + 5 = 3(sin^2 t)/(cos^2 t)`
`(1 + 5cos^2 t)/(cos^2 t) = (3sin^2 t)/(cos^2 t)`
Simplify both sides by `cos^2 t.`
Replace in the equation `3sin^2 t` by `(3 - 3cos^2 t)`-->
`1 + 5cos^2 t = 3 - 3cos^2 t`
`8cos^2 t = 2` --> `cos^2 t = 2/8 = 1/4`
`cos t = +- 1/2`
Trig table and unit circle -->
`cos t = +- 1/2` --> `t = +- pi/3`
General answer:
`t = +- pi/3 + 2kpi`