Sin 2 Cos 2

Sin 2 Cos 2. sin2 + cos2 = 1 (1) 1 + cot2 = cosec2 (2) tan2 + 1 = sec2 (3) Note that (2) = (1)=sin 2 and (3) = (1)=cos Compoundangle formulae cos(A+ B) = cosAcosB sinAsinB (4) cos(A B) = cosAcosB+ sinAsinB (5) sin(A+ B) = sinAcosB+ cosAsinB (6) sin(A B) = sinAcosB cosAsinB (7) tan(A+ B) = tanA+ tanB 1 tanAtanB (8) tan(A B) = tanA tanB 1 + tanAtanB (9).

Trigonometric Proof – sin^2 + cos^2 = 1 The most fundamental of all trigonometric identities ‘sin^2 (x) + cos^2 (x) = 1’ a basis of many other proofs So before moving on let’s prove the proof which will prove our proofs! Below is a diagram using Pythagoras’ Theorem to prove the identity Below the diagram is an explanation if you get stuck or confused.

Trigonometric Identities Purplemath

sin 2 ⁡ (x) cos 2 ⁡ (x) = (sin ⁡ (x) cos ⁡ (x)) 2 = sin 2 ⁡ (2 x) 4 Reduce the power 1 − cos ⁡ (4 x) 8 and announce the result x 8 − sin ⁡ (4 x) 32 + C.

Trigonometric Identities

Basic and Pythagorean Identities csc⁡(x)=1sin⁡(x)\\csc(x) = \\dfrac{1}{\\sin(x)}csc(x)=sin(x)1​ sin⁡(x)=1csc⁡(x)\\sin(x) = \\dfrac{1}{\\csc(x)}sin(x)=csc(x)1​ AngleSum and Difference Identities sin(α + β) = sin(α) cos(β) + cos(α) sin(β) sin(α – β) = sin(α) cos(β) – cos(α) sin(β) cos(α + β) = cos(α) cos(β) – sin(α) sin(β) DoubleAngle Identities sin(2x) = 2 sin(x) cos(x) cos(2x) = cos2(x) – sin2(x) = 1 – 2 sin2(x) = 2 cos2(x) – 1 tan⁡(2x)=2tan⁡(x)1−tan⁡2(x)\\tan(2x) = \\dfrac{2 \\tan(x)}{1 \\tan^2(x)}tan(2x)=1−tan2(x)2tan(x)​ HalfAngle Identities sin⁡(x2)=±1−cos⁡(x)2\\sin\\left(\\dfrac{x}{2}\\right) = \\pm \\sqrt{\\dfrac{1 \\cos(x)}{2}}sin(2x​)=±21−cos(x)​​ cos⁡(x2)=±1+cos⁡(x)2\\cos\\left(\\dfrac{x}{2}\\right) = \\pm \\sqrt{\\dfrac{1 + \\cos(x)}{2}}cos(2x​)=±21+cos(x)​​.