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If f(x) = [(cos theta, - sin theta, 0),(...

If `f(x) = [(cos theta, - sin theta, 0),(sin x, cos x , 0),(0,0,1)]`, show that `F(x) F(y) = F(x + y)`.

Answer

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Knowledge Check

  • If A= [[cos x,sin x,0],[-sin x,cos x,0],[0,0,1]]=f(x) then A^-1=

    A
    `f(-x)`
    B
    `f(x)`
    C
    `-f(x)`
    D
    `-f(-x)`

  • If the matrix [[cos theta,sin theta,0],[sin theta,cos theta,0],[0,0,1]] is singular then theta=

    A
    `pi`
    B
    `(pi)/(2)`
    C
    `(pi)/(3)`
    D
    `(pi)/(4)`

  • If x = a(cos theta + theta sin theta), y = a (sin theta - theta cos theta), (dy)/(dx) =

    A
    `cot theta`
    B
    `tan theta`
    C
    `tan.(theta)/(2)`
    D
    `cot.(theta)/(2)`

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    The centroid of a triangle formed by the points (0, 0), (cos theta, sin theta) and (sin theta, -cos theta) lies on the line y=2x . Then theta is :

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