Home / Tổng Hợp / sin^2x.cos^2x bằng gì Sin^2x.cos^2x bằng gì 10/08/2021 Sin 2x cos 2x is one of the trigonometric identities which is essential for solving a variety of trigonometry related questions. Here, the simplified value of Sin2x cos2x is given along with the integral và derivative of sin2x & cos 2x.What is the Value of Sin 2x Cos 2x?The value of sin 2x × Cos 2x is:Bạn đang xem: Sin^2x.cos^2x bằng gìHow to lớn Derive Sin 2x Cos 2x Value?To find the value of sin2x × Cos 2x, the trigonometric double angle formulas are used. For the derivation, the values of sin 2x & cos 2x are used.From trigonometric double angle formulas,Sin 2x = 2 sin x cos x ————(i)And,Cos 2x = Cos2x − Sin2x= 2 cos2x − 1 ————(ii) = 1 − 2Sin2x ————(iii)Also Check: TrigonometryNow, khổng lồ get the value of Sin 2x Cos 2x, multiply equation (i) with (ii) or (i)Consider equation (i) and (ii),Sin 2x = 2 sin x cos xAnd,Cos 2x = 2 cos2x − 1Multiply them to get,Sin 2x Cos 2x = 2 Sin x Cos x (2 cos2x − 1)= 4 Sin x Cos3 x − 2 Sin x Cos x= 2 Cos x (2 Sin x Cos2 x − Sin x)Now, consider equation (i) và (iii),Sin 2x = 2 sin x cos xAnd,Cos 2x = 1 − 2 Sin2xMultiply them to get,Sin 2x Cos 2x = 2 Sin x Cos x (1 − 2 Sin2x)= 2 Sin x Cos x − 4 Sin3 x Cos x= 2 Cos x (Sin x – 2 Sin3 x)So,Sin 2x Cos 2x = 2 Cos x (2 Sin x Cos2 x − Sin x)Or,Sin 2x Cos 2x = 2 Cos x (Sin x – 2 Sin3 x)Derivative of Sin 2x Cos 2xd/dx (Sin 2x Cos 2x) = 2Cos(4x)Proof:Sin(2x)cos(2x)= ½(2sin(2x)cos(2x))Or, ½Sin(4x)Now, differentiate the given function w.r.t. x:d/dx <½Sin(4x)>= ½= ½= ½So, d/dx (Sin 2x Cos 2x) = 2 Cos(4x)Integral of Sin 2x Cos 2xXem thêm: So Sánh Quá Trình Phiên Mã Ở Sinh Vật Nhân Sơ Và Sinh Vật Nhân Thực Là∫ (Sin 2x Cos 2x) = (Sin 2x)2/ 4 + CProof:Consider sin 2x = uSo, du/dx = 2Cos(2x)Or, dx = du/2Cos(2x)Now, ∫u Cos(2x)dx = ∫u • Cos(2x) • du/2cos 2xHere, Cos 2x can be cancelled out.So,∫u Cos(2x)dx = ∫(u • du/2)= ½<∫u du>= ½ u2/2 + c= u2/4 + COr, ∫ (Sin 2x Cos 2x) = (Sin 2x)2/ 4 + CLearn More:Trigonometry FormulasTrigonometric FunctionsTrigonometry TableHalf Angle formulas