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[sin(pi/2-x) + sin(pi-x)]^2+[(cos((3pi)/...

`[sin(pi/2-x) + sin(pi-x)]^2+[(cos((3pi)/2-x)+cos(2pi-x)]^2=`

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Prove that: (a) (cos(pi+x) cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x (b) cos((3pi)/2 + x)cos(2pi+x){cot ((3pi)/2-x)+cot(2pi+x)}=1

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Knowledge Check

  • The value of ((cos(x/2+x)+sin(pi/2+x))/(cos(pi/2-x)-sin(pi/2-x)))^2 is

    A
    `(1-sin 2x)/(1+sin 2x)`
    B
    `(1+sin 2x)/(1-sin2x)`
    C
    1
    D
    None of these

  • The value of ((cos(x/2+x)+sin(pi/2+x))/(cos(pi/2-x)-sin(pi/2-x)))^2 is

    A
    `(1-sin 2x)/(1+sin 2x)`
    B
    `(1+sin 2x)/(1-sin2x)`
    C
    1
    D
    None of these

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    Explore conceptually related problems

    (cos(pi-x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x

    (cos (pi + x) cos (-x)) / (sin (pi-x) cos ((pi) / (2) -x)) = cot ^ (2) x

    (cos(pi-x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^(2)x

    sin m((pi)/(2)+x)+cos n((pi)/(2)-x)

    (cos (pi+x).cos(-x))/(sin(pi-x).cos(pi/2+x)) = cot^2x

    Prove that (cos(pi+x)cos(-x))/(sin(pi-x)cos((pi)/(2)+x))=cot^(2)x

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