Question

Solve the equation `tan^2x=3(3-secx)`, if `x` lies in interval `[0^@,360^@)`?

Answer 1

`x` is `60^@, 101.5^@, 258.5^@` or `300^@`

Explanation:

As `tan^2x=3(3-secx)`, we have

`sec^2x-1=9-3secx`

or `sec^2x+3secx-10=0`

or `(secx+5)(secx-2)=0`

Hence `secx=-5` or `secx=2` and using tables

`cosx=-0.2=cos101.5^@` and `cos258.5^@`

or `cosx=0.5=cos60^@` and `cos300^@`

(as `cos(360^@-A)=cosA`)

Hence, `x` is `60^@, 101.5^@, 258.5^@` or `300^@`