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Q. If a cos2 θ + b sin2 θ = c has α and β as its roots, the prove that tanα +tan β = 2b/a+c

Q. If a cos2θ  + b sin2θ  = c has α and β as its roots, the prove that 
tanα +tanβ = 2b/a+c
 

    Grade:11

    1 Answers

    Arun
    25763 Points
    2 years ago
    Dear Naman
     
    a (1- tan² theta/1 + tan² theta) + b ( 2tan theta/1 + tan² theta) = c
    Now I am writing tan theta as t
    a (1 - t²) + b (2t) = c (1+t²)
    (a+c) t² + 2b t  + (a-c) = 0
    As alpha and beta are roots, hence
    tan alpha + tan beta = 2b/a +c

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