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    Maths-
    General
    Easy

    Question

    I n space triangle A B C comma space i f space x equals tan invisible function application left parenthesis left parenthesis B minus C right parenthesis divided by 2 right parenthesis tan invisible function application A divided by 2 comma y equals tan invisible function application left parenthesis left parenthesis C minus A right parenthesis divided by 2 right parenthesis tan invisible function application B divided by 2 comma z equals tan invisible function application left parenthesis left parenthesis A minus B right parenthesis divided by 2 right parenthesis tan invisible function application C divided by 2 space t space h space e n space x plus y plus z space
    in terms  terms only  is

    1. x y z
    2. 2x y z
    3. -x y z
    4. 1 divided by 2 space x y z

    The correct answer is: -x y z

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    n space triangle A B C space left parenthesis c o t invisible function application A divided by 2 plus c o t invisible function application B divided by 2 plus c o t invisible function application C divided by 2 right parenthesis divided by left parenthesis c o t invisible function application A plus c o t invisible function application B plus c o t invisible function application C right parenthesis equals

    n space triangle A B C space left parenthesis c o t invisible function application A divided by 2 plus c o t invisible function application B divided by 2 plus c o t invisible function application C divided by 2 right parenthesis divided by left parenthesis c o t invisible function application A plus c o t invisible function application B plus c o t invisible function application C right parenthesis equals

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    I n space triangle A B C comma space i f space x equalstan invisible function application left parenthesis left parenthesis B minus C right parenthesis divided by 2 right parenthesis tan invisible function application A divided by 2 comma y equals tan invisible function application left parenthesis left parenthesis C minus A right parenthesis divided by 2 right parenthesis tan invisible function application B divided by 2 comma z equals tan invisible function application left parenthesis left parenthesis A minus B right parenthesis divided by 2 right parenthesis tan invisible function application C divided by 2 space t space h space e n space x plus y plus z space i n space t e r m s space left parenthesis x comma y comma z space t e r m s space o n l y space right parenthesis space i s

    I n space triangle A B C comma space i f space x equalstan invisible function application left parenthesis left parenthesis B minus C right parenthesis divided by 2 right parenthesis tan invisible function application A divided by 2 comma y equals tan invisible function application left parenthesis left parenthesis C minus A right parenthesis divided by 2 right parenthesis tan invisible function application B divided by 2 comma z equals tan invisible function application left parenthesis left parenthesis A minus B right parenthesis divided by 2 right parenthesis tan invisible function application C divided by 2 space t space h space e n space x plus y plus z space i n space t e r m s space left parenthesis x comma y comma z space t e r m s space o n l y space right parenthesis space i s

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    Two sides of triangle are given by equation  and angle between
    the sides is pi divided by 3. Then perimeter of the triangle is

    Two sides of triangle are given by equation  and angle between
    the sides is pi divided by 3. Then perimeter of the triangle is

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    I n a triangle A B C comma a left parenthesis c o s squared invisible function application B plus c o s squared invisible function application C right parenthesis plus c o s invisible function application A left parenthesis c c o s invisible function application C plus b c o s invisible function application B right parenthesis equals

    I n a triangle A B C comma a left parenthesis c o s squared invisible function application B plus c o s squared invisible function application C right parenthesis plus c o s invisible function application A left parenthesis c c o s invisible function application C plus b c o s invisible function application B right parenthesis equals

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    left parenthesis I n space triangle A B C comma left parenthesis cos invisible function application C plus cos invisible function application A right parenthesis divided by left parenthesis c plus a right parenthesis plus left parenthesis cos invisible function application B right parenthesis divided by b equals & right parenthesis

    left parenthesis I n space triangle A B C comma left parenthesis cos invisible function application C plus cos invisible function application A right parenthesis divided by left parenthesis c plus a right parenthesis plus left parenthesis cos invisible function application B right parenthesis divided by b equals & right parenthesis

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    I n space capital delta A B C sum a cubed c o s invisible function application left parenthesis B minus C right parenthesis equals

    I n space capital delta A B C sum a cubed c o s invisible function application left parenthesis B minus C right parenthesis equals

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    I n space a n y space triangle A B C left parenthesis left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis right parenthesis divided by left parenthesis 4 b squared c squared right parenthesis

    I n space a n y space triangle A B C left parenthesis left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis right parenthesis divided by left parenthesis 4 b squared c squared right parenthesis

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    142 I n triangle A B C sum a cubed S i n invisible function application left parenthesis B minus C right parenthesis equals

    142 I n triangle A B C sum a cubed S i n invisible function application left parenthesis B minus C right parenthesis equals

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    I n space triangle A B C comma sum a left parenthesis sin invisible function application B minus sin invisible function application C right parenthesis equals

    I n space triangle A B C comma sum a left parenthesis sin invisible function application B minus sin invisible function application C right parenthesis equals

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    The perimeter of a ΔA B C space is 6 times the A.M of the sines of its angles if the side '  is , then the angle  is

    The perimeter of a ΔA B C space is 6 times the A.M of the sines of its angles if the side '  is , then the angle  is

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    The angles of a triangle are in the ratio 3:5:10. Then ratio of smallest to greatest side is

    The angles of a triangle are in the ratio 3:5:10. Then ratio of smallest to greatest side is

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    If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

    If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

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    The sides of a triangle are sin invisible function application alpha comma cos invisible function application alpha spaceand √ left parenthesis 1 plus sin invisible function application alpha cos invisible function application alpha right parenthesis for some 0 less than alpha less than pi divided by 2.Then the greatest angle of the triangle is

    The sides of a triangle are sin invisible function application alpha comma cos invisible function application alpha spaceand √ left parenthesis 1 plus sin invisible function application alpha cos invisible function application alpha right parenthesis for some 0 less than alpha less than pi divided by 2.Then the greatest angle of the triangle is

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    If the sides of a triangle are in the ratio x colon y colon √ left parenthesis x squared plus x y plus y squared right parenthesis then greatest angle is

    If the sides of a triangle are in the ratio x colon y colon √ left parenthesis x squared plus x y plus y squared right parenthesis then greatest angle is

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    In triangle A B C comma i f c squared equals a squared plus b squared comma 2 s equals a plus b plus c then 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals

    In triangle A B C comma i f c squared equals a squared plus b squared comma 2 s equals a plus b plus c then 4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals

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