Question

Simplify sec^2x+sec^2x*tan^2x

Answer 1

`sec^(4)` x

Explanation:

Using the trigonometric identities

sec x =
`(1)/(cosx)`, tan x =
`(sinx)/(cosx)`, then

sec²x +
`(1)/(cos^2x)` ×
`(sin^2x)/(cos^2x)`

= sec²x +
`(sin^2x)/(cos^(4x) )`

=
`(1)/(cos^2x)` +
`(sin^2x)/(cos^(4 ) x)`

=
`(cos^2x+sin^2x)/(cos^(4)x )`

=
`(1)/(cos^(4)x )` =
`sec^(4)` x