Question

If \[sec\theta + tan\theta = x\] then \[tan\theta =\] 

पर्याय

• \[\frac{x^2 + 1}{x}\]

• \[\frac{x^2 - 1}{x}\]

• \[\frac{x^2 + 1}{2x}\]

• \[\frac{x^2 - 1}{2x}\] 

Answer 1

Given: 

`sec θ+tanθ=x` 

We know that,

`sec^2 θ-tan^2 θ=1`

⇒` (sec θ+tan θ)(sec θ-tanθ)=1` 

⇒`x(sec θ-tan θ)=1`

⇒ `secθ-tan θ=1/x` 

Now, 

`secθ+tan θ=x,` 

`sec θ-tan θ=1/x`

Subtracting the second equation from the first equation, we get 

`(secθ+tan θ)-(secθ-tanθ)=x-1/x` 

⇒` secθ+tanθ-secθ+tanθ=(x^2-1)/x`  

⇒ `2 tanθ=(x^2-1)/x` 

⇒ `2 tan θ=(x^2-1)/(2x)` 

⇒ `tan θ=(x^2-1)/(2x)`