Cos2a formula
Cos 2a : 1 – cos 2a is equal to what ? There are some important trigonometric identities which are known as double angle formula like Sine 2x, Cosine 2x, Tangent 2x because these trigonometric identities have double angles in them. We will understand this formula through solved examples. Cos 2 A = Cos2A – Sin2A = 2Cos2A – 1 = 1 – 2sin2A
We can easily drive 1 – Cos 2a is equal to 2sin2A formula by using sum formulas of trigonometry. Some formula can be derived by using Pythagorean identities. There are some important addition formulas of trigonometry –
- sin (A + B) = sin A cos B + cos A sin B
- cos (A + B) = cos A cos B – sin A sin B
- tan (A + B) = (tan A + tan B) / (1 – tan A tan B)
Cos 2a, Sin 2a and Tan 2a Double Angle Formulas
We must know the addition formula of trigonometry cos (A + B) = cos A cos B – sin A sin B to find the 1 – Cos 2a is equal to 2sin2A. In this formula, we will put A = B the formula will become, cos (A + A) = cos A cos A – sin A sin A = cos 2A = cos2A – sin2A.
Now we will use Pythagorean identity sin2A + cos2A = 1 to drive 1 – Cos 2a is equal to 2sin2A formula. We will drive cos 2A formula by using Pythagorean identity sin2A + cos2A = 1. There are two other formulas of cos 2A trigonometric function can be derived as well.
- (i) cos 2A = cos2A − (1 − cos2A) = 2cos2A – 1
- (ii) cos 2A = (1- sin2A) – sin2A = 1 – 2sin2A
By using cos 2A formula = (1- sin2A) – sin2A = 1 – 2sin2A we can find 1 – Cos 2a is equal to 2sin2A formula derivation.
- cos 2A = (1- sin2A) – sin2A = 1 – 2sin2A
- cos 2A = 1 – 2sin2A
- 1 – cos 2A = 2sin2A
Cos 2a formula, Sin 2a and Tan 2a Double Angle Formulas. Please follow this link of Explanation of Mathematics formula – Click
- sin 2A = 2 sin A cos A (or) (2 tan A) / (1 + tan2A)
- cos 2A = cos2A – sin2A (or) 2cos2A – 1 (or) 1 – 2sin2A (or) (1 – tan2A) / (1 + tan2A)
- tan 2A = (2 tan A) / (1 – tan2A)
cos 2A = cos2A – sin2A (or) 2cos2A – 1 (or) 1 – 2sin2A (or) (1 – tan2A) / (1 + tan2A)
Sin 2A/(1+cos2A)=tanA
cos 2A = cos2A – sin2A (or) 2cos2A – 1 (or) 1 – 2sin2A (or) (1 – tan2A) / (1 + tan2A)
sin 2A = 2 sin A cos A (or) (2 tan A) / (1 + tan2A)
tan 2A = (2 tan A) / (1 – tan2A)
cos2A−sin2A=2cos2A−1
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