Question

How do I solve 2sec^2x + tan^2x-3=0 ?

Answer 1

See below

Explanation:

Apply trig identity:
`1+tan^2x=sec^2x`

So:
`2sec^2x + tan^2x-3=0`

`2(1+tan^2x)+tan^2x-3=0`

`2+2tan^2x+tan^2x-3=0`

`3tan^2x-1=0`

`tan^2x=1/3`

`tanx= +-sqrt3/3`

`x=pi/6+-pin`
`x= (5pi)/6+-pin`
Where n is an element of all real numbers

graph{2(secx)^2+(tanx)^2-3 [-10, 10, -5, 5]}