Prove that: `s in" "3x" "+" "s in" "2x" "" "s in" "x" "=" "` `4" "s in" "x" "cos` `x/2` `cos` `(3x)/2`

Prove that: sin" "3x" "+" "sin" "2x" "+" "sin" "x" "=" " 4" "sin" "x" "cos x/2 cos (3x)/2

Prove that: (i) sin 3x+"sin" 2x-"sin" x = 4 sin x cos((x)/(2))cos((3x)/(2)) (ii) ("sin" 3x+"sin" x)"sin" x+(cos 3x-cos x)cos x=0.

Prove that (sin 3x - sin x) /( cos x - cos 3x) = cot 2x

Prove that: (s in5x-2s in3x+s in x)/(cos5x-cos x)=tan x

Prove that ( " cos " 4x + " cos " 3x + " cos " 2x)/(" sin " 4x + " sin " 3x + " sin " 2x) = " cot 3x

Prove that sin 3x . sin^(3) x+cos 3 x . Cos^(3)x=cos^(3) 2x

Prove that: s in3x+s in2x-s in x=4s in x(cos x)/(2)(cos(3x))/(2)

Prove that: cos^(2)2x-cos^(2)6x=s in4xs in8x

Prove that: s in x+s in3x++sin(2n-1)x=(sin^(2)nx)/(s in x) for all n in N.

Prove that sin3x+sin2x-sinx=4sinxcos(x/2)cos((3x)/2)