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sum(r=1)^n (cos(2r x))/sin(r x+pi/4)=((2...

`sum_(r=1)^n (cos(2r x))/sin(r x+pi/4)=((2sin50 x)/sin(x/2))sin(pi/4-(m x)/2)` then

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If sum _(r =1) ^(n) (cos (2rx))/(sin (r x + (pi)/(4)))= (2 sin (50x)sin ((pi)/(4)- (101)/(2)))/(sin ((x)/(2))) then value of n is "_________"

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

Knowledge Check

  • int_(pi)^(5pi//4) (sin 2x)/(cos^(4) x +sin^(4)x) dx =

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

  • cos^(2)""((pi)/(4) +x ) - sin^(2) ""((pi)/4- x ) =

    A
    0
    B
    `-1`
    C
    `1`
    D
    2

  • Cos^(2)((pi)/(4)+x)-Sin^(2)((pi)/(4)-x)=

    A
    -1
    B
    0
    C
    1
    D
    2

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    cos ^ (2) (pi / 4 + x) -sin ^ (2) (pi / 4-x)

    Prove that sum_(r=0)^(n)C_(r)sin rx cos(n-r)x=2^(n-1)sin(nx)

    For x in(0,(pi)/(4)). Let S_(n)=sum_(r=1)^(2n)sin(sin^(-1)x^(3r-2)),C_(n)=sum_(r=1)^(2n)cos(cos^(-1)x^(3r-1)) and T_(n)=sum_(r=1)^(2n)tan(tan^(-1)x^(3r)) where n in N and n>=3

    prove that sin((pi)/(4)+x)+sin((pi)/(4)-x)=sqrt(2)cos x

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