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If cos alpha + cos beta = 1//2 and sin a...

If `cos alpha + cos beta = 1//2 and sin alpha + sin beta = 1//3,` then

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If alpha, beta are the solutions of the equation a cos theta + b sin theta = c , where a, b, c in R and if a^(2) + b^(2) gt 0, cos alpha ne cos beta and sin alpha ne sin beta , then show that sin alpha.sin beta= (c^(2) - a^(2))/(a^(2) + b^(2))

If alpha, beta are the solutions of the equation a cos theta + b sin theta = c , where a, b, c in R and if a^(2) + b^(2) gt 0, cos alpha ne cos beta and sin alpha ne sin beta , then show that sin alpha + sin beta = (2bc)/(a^(2) + b^(2))

Knowledge Check

  • If cos alpha + cos beta = 3/2 and sin alpha + sin beta = 1/2 and theta is the arithmetic mean of alpha and beta then sin 2 theta + cos 2 theta

    A
    `3/5`
    B
    `4/5`
    C
    `7/5`
    D
    `8/5`

  • If cos alpha + cos beta = a, sin alpha + sin beta = b and theta is the arithmetic mean between alpha and beta then sin 2 theta + cos 2 theta is equal to

    A
    `(a+b)^(2)//(a^(2)+b^(2))`
    B
    `(a-b)^(2)//(a^(2)+b^(2))`
    C
    `(a^(2)-b^(2))//(a^(2)+b^(2))`
    D
    none of these

  • If cos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha - beta )=

    A
    0
    B
    `1`
    C
    `-1`
    D
    2

    • Similar Questions

    Explore conceptually related problems

    If alpha, beta are the solutions of the equation a cos theta + b sin theta = c , where a, b, c in R and if a^(2) + b^(2) gt 0, cos alpha ne cos beta and sin alpha ne sin beta , then show that cos alpha + cos beta = (2bc)/(a^(2)+b^(2))

    sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of sin (alpha + beta) is

    sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of cos ( alpha + beta) is

    sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of tan (alpha + beta) is

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