Question

If θ is an acute angle such that sec² θ = 3, then the value of \[\frac{\tan^2 \theta - {cosec}^2 \theta}{\tan^2 \theta + {cosec}^2 \theta}\]

पर्याय

• \[\frac{4}{7}\]

• \[\frac{3}{7}\]

• \[\frac{2}{7}\]

• \[\frac{1}{7}\]

Answer 1

Given that:

`sec^2θ=3` 

`secθ=sqrt3` 

We need to find the value of the expression 

`(tan^2θ-cosec^2θ)/(tan^2θ+cosec^2θ)` 

`"since"  secθ="Hypotenuse"/"Base"`. so 

⇒` "Hypotenuse"= sqrt3` 

⇒ `"Base"=1`  

⇒ `"Perpendicular"=sqrt(3-1)`  

⇒ `"Perpendicular"=sqrt2` 

Here we have to find:  `(tan^2θ-cosec^2θ)/(tan^2θ+cosec^2θ)` 

⇒`(tan^2θ-cosec^2θ)/(tan^2θ+cosec^2θ) = (2/1-3/2)/(2/1+3/2)`  

⇒`(tan^2θ-cosec^2θ)/(tan^2θ+cosec^2θ)=(1/2)/(7/2)` 

⇒`(tan^2θ-cosec^2θ)/(tan^2θ+cosec^2θ)=1/7`