Question

If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of  `"sec" theta + "tan" theta` is ____________.

Options

• only 2x

• only `1/(2"x")`

• 2x or `1/(2 "x")`

• None of these

Answer 1

If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of  `"sec" theta + "tan" theta` is `underline(2"x or" 1/(2 "x"))`.

Explanation:

`"sec" theta = "x" + 1/(4"x"), "x" in "R", "x" ne 0,`

`"sec" theta = "x" + 1/ (4"x")`

`=> "tan" theta = sqrt ("sec"^2 theta - 1) = sqrt (("x" + 1/4"x")^2 - 1)`

`=> "tan" theta = sqrt ("x"^2 + 1/(4 "x")^2 + 1/2 - 1) = sqrt (("x" + 1/(4 "x"))^2`

`"tan" theta = ("x" - 1/(4"x"))`

`=> "tan" theta = "x" - 1/(4"x"), "x" in "R", "x" ne 0, =>`

`"sec" theta + "tan" theta = "x" + 1/(4"x") + "x" - 1/(4 "x") = 2 "x"`

When we will take the negative value with tan we will get an answer as 1/2x.