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Show that the solution of cos theta - si...

Show that the solution of `cos theta - sin theta = -1` is `2npi pm (3pi)/(4) - (pi)/(4), n in Z`

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The correct Answer is:
`2npi pm (3pi)/(4) - (pi)/(4)`
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Knowledge Check

  • The number of solutions of cos 2 theta = sin theta in (0 , 2 pi ) is

    A
    A. 4
    B
    B. 3
    C
    C. 2
    D
    D. 5

  • The number of solutions of cos 2 theta = sin theta in (0, 2pi) is

    A
    4
    B
    3
    C
    2
    D
    5

  • I : The solution of the simultaneous equations sin theta = 1//2, tan theta = 1//sqrt(3) is {2n pi+pi//6 : n in Z} II : The solution of the simultaneous equations cos theta = - 1//sqrt(2), tan theta = -1 is {2n pi + 3pi//4 : n in Z}

    A
    only I is true
    B
    only II is true
    C
    both I and II are true
    D
    neither I or II are true

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    A : The general solution for cos theta = 3//2 is theta = 2n pi pm Cos^(-1)(3//2) R : The general solution for cos theta = k is theta = 2n pi pm alpha, n in Z where 'alpha' is principal value, alpha in [0, pi] and |k|le 1

    The solution set of (5+4 cos theta) (2 cos theta + 1) =0 in the interval [0, 2pi] is

    The sum of all the solutions of cot theta = sin 2 theta (theta ne n pi, n " integer"), 0 le theta le pi . is

    If |2 sin theta - cos ec theta| ge 1 and theta ne (n pi)/(2), n in Z , then

    S_(1) : If tan p theta = cot q theta " then " theta = ((2 n + 1) pi)/( p (P + q)), n in Z S_(2) : If tan (pi sin theta ) = cot (pi cos theta) , " then " sin (theta + (pi)/(4)) = pm (1)/(2 sqrt(2))

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