Question

If sec θ + tan θ = x, then sec θ =

Options

• \[\frac{x^2 + 1}{x}\]

• \[\frac{x^2 + 1}{2x}\]

• \[\frac{x^2 - 1}{2x}\]

• \[\frac{x^2 - 1}{x}\]

Answer 1

Given:  `sec θ+tan θ=1` 

We know that, 

`sec^2θ-tan^2θ=1` 

⇒ `(secθ+tan θ)(secθ-tan θ)=1` 

⇒`x(sec θ-tan θ)=1` 

⇒ `secθ-tan θ=1/x` 

Now, 

`sec θ+tan =x` 

`sec θ-tan θ=1/x` 

Adding the two equations, we get 

`(sec θ+tan θ)+(sec θ-tan θ)=x+1/x` 

⇒` sec θ+tan θ+sec θ-tan θ=(x^2+1)/x` 

⇒ `2 sec θ=(x^2+1)/x` 

⇒` sec θ=(x^2+1)/(2x)`