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

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)

lim_(xto(pi)) (1-sin(x/2))/(cos(x/2)(cos(x/4)-sin(x/4)))

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

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