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Prove that the equation cos 2x + a sin x...

Prove that the equation `cos 2x + a sin x = 2a - 7` possesses a solution if `2 le a le 6`.

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Knowledge Check

  • The equation sin^6 x + cos^6 x = k possesses solution if

    A
    `k ge 1`
    B
    `1/4 lt k lt1`
    C
    `1/4 le k lt 1`
    D
    `1/4 le k le 1`

  • If -3 le x le 3 and x is an integer. The solution of x+2 lt 1 is

    A
    `-3,-2`
    B
    `-2,-1`
    C
    `-1,0`
    D
    `-2,0`

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