Question

lf alpha and Beta are the roots of the equation alpha COS 2 theta + beta Sin2theta=b, then prove that tan alpha+tan beta=2b/a+c​

Answer 1

Step-by-step explanation:

ANSWER

Given,

acos2θ+bsin2θ=c

⇒  a(1+tan2θ1−tan2θ)+b(1+tan2θ2tanθ)=c

⇒  a(1−tan2θ)+2btanθ=c(1+tan2θ)

α and β are roots then,

⇒  a(1−tan2α)+2btanα=c(1+tan2α)       ----- ( 1 )

⇒  a(1−tan2β)+2btanβ=c(1+tan2β)       ----- ( 2 )

Subtracting ( 2 ) from ( 1 ),

⇒  a(1−tan2α)+2btanα−[a(1−tan2β)+2btanβ]=c(1+tan2α)−c(1+tan2β)

⇒  −a(tan2α−tan2β)+2b(tanα−tanβ)=c(tan2α−tan2β)