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If `alpha and beta` are two solutions of the equation `a tan x + b sec x=c`, then find the values of `sin (alpha+beta) and cos (alpha+beta)`

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Knowledge Check

  • If tan alpha and tan beta are the roots of the equation x^(2) +px + q = 0 , then the value of sin^(2) (alpha +beta) + p cos (alpha + beta) sin (alpha + beta) + q cos^(2) (alpha + beta) is

    A
    p + q
    B
    p
    C
    q
    D
    `(p)/(p +q)`

  • If alpha and beta are the solutions of the equation a tan theta + b sec theta =c , then tan ( alpha + beta)=

    A
    `( 2ab )/( a^(2) - b^(2))`
    B
    `( 2ab)/(a^(2) + b^(2))`
    C
    `( 2ac)/( a^(2) - c^(2))`
    D
    `( 2bc)/( b^(2) - c^(2))`

  • If tan alpha and tan beta are the roots of the equation x^2 +px + q=0 , then the value of sin^2 (alpha + beta) + pcos(alpha + beta) sin(alpha + beta) + qcos^2 (alpha + beta) is

    A
    p+q
    B
    p
    C
    q
    D
    `p/(p+q)`

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