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Evaluate |[cos theta, -sin theta], [sin ...

Evaluate `|[cos theta, -sin theta], [sin theta, cos theta]|`

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Given determinant = `cos^2 theta + sin^2 theta = 1`
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If A=[[cos theta, sin theta],[ -sin theta, cos theta]] , then prove that A^n=[[cos ntheta, sinn theta],[ -sin n theta, cos n theta]] , n in N .

Show that [[1 , -tan theta ],[ tan theta, 1]][[1, tan theta],[ -tan theta, 1]]^(-1)=[[cos 2 theta, -sin 2 theta],[ sin 2 theta, cos 2 theta]]

Knowledge Check

  • The product of matrices A = [(cos^(2) theta, cos theta sin theta),(cos theta sin theta , sin^(2) theta)] and sin B = [(cos^(2)phi, cos phi sin phi),(cos phi sin phi, sin^(2) phi)] is a null matrix if theta - phi =

    A
    `2 n pi, n in Z`
    B
    `n (pi)/(2), n in Z`
    C
    `(2n+ 1) (pi)/(2) , n in Z`
    D
    `n pi, n in Z`

  • The normal to the curve x = a (cos theta + theta sin theta), y = a (sin theta - theta cos theta) at any point theta

    A
    passes through the origin.
    B
    makes an angle `pi//2 + theta` with the x-axis.
    C
    passes through `(a (pi)/(2), - a)`
    D
    is at a constant distance from the origin.

    • Similar Questions

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    If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2=[[cos2theta,sin2theta],[-sin2theta,cos2theta]]

    If x and y are connected parametrically by the equation without eliminating the parameter, find (dy/dx) if x=a(cos theta+theta sin theta) y=a(sin theta-theta cos theta)

    If a cos theta+b sin theta=c , show that asin theta-bcos theta=pm sqrt((a)^(2)+(b)^(2)-(c)^(2))

    (b)Show that (sin theta+sin 3theta+sin 5 theta+sin 7 theta)/(cos theta+cos3theta+cos 5 theta+cos 7 theta)=tan 4 theta .

    If cos theta =7/25 and theta is an angle in the fourth quadrant, find the value of (25 cos theta -7 tan theta)/(cos theta-sin theta) .

    Solve sqrt 2+sin theta=cos theta .

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