let α & β be two real roots of the equation $$k+1tan2x$$−$$2$$.λ$$tanx=1$$−k, where k≠−$$1and$$ λare real numbers. If $$tan2$$α$$+$$β$$=50$$ then the value of λ is

Question

let  α & β be two real roots of the equation $$k+1tan2x$$−$$2$$.λ$$tanx=1$$−k, where  k≠−$$1and$$  λare real numbers. If  $$tan2$$α$$+$$β$$=50$$ then  the value of  λ is

Infinity Learn · Accepted Answer

Given that $$tan$$α and $$tan$$β are roots of the $$equationk+1tan2x$$−$$2$$λ $$tanx+k$$−$$1=0$$⇒sum of roots $$=$$ $$tan$$α$$+$$$$tan$$β$$=2$$λ$$k+1and$$, product of roots $$=$$ $$tan$$α$$tan$$β$$=k$$−$$1k+1Now$$ $$tan$$α$$+$$β$$=$$$$tan$$α$$+$$$$tan$$β$$1-$$$$tan$$α$$tan$$β$$=2$$λ$$k+11$$−k−$$1k+1=2$$λ$$2=$$λ$$2$$⇒$$tan2$$α$$+$$β$$=$$λ$$22=50$$⇒λ$$=10$$

let $α & β$ be two real roots of the equation $(k + 1) \tan^{2} x - \sqrt{2} . λ \tan x = (1 - k)$ , where $k (\neq - 1)$ and $λ$ are real numbers. If $\tan^{2} (α + β) = 50$ then the value of $λ$ is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

let α & β be two real roots of the equation k+1tan2x−2.λtanx=1−k, where k≠−1and λare real numbers. If tan2α+β=50 then the value of λ is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

let $α & β$ be two real roots of the equation $(k + 1) \tan^{2} x - \sqrt{2} . λ \tan x = (1 - k)$ , where $k (\neq - 1)$ and $λ$ are real numbers. If $\tan^{2} (α + β) = 50$ then the value of $λ$ is