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Now, we will prove the half angle formula for the cosine function. Using one of the above formulas of cos A, cos A = 2 cos2(A/2) – 1 From this, 2 cos2(A/2) = 1 + cos A cos2 (A/2) = (1 + cos A) / 2 cos (A/2) = ±√[(1 + cos A) / 2]

Now, we will prove the half angle formula for the sine function. Using one of the above formulas of cos A, we have cos A = 1 – 2 sin2 (A/2) From this, 2 sin2 (A/2) = 1 – cos A sin2 (A/2) = (1 – cos A) / 2 sin (A/2) = ±√[(1 – cos A) /… Continue reading Half Angle Formula of Sin Proof

In this section, we will see the half angle formulas of sin, cos, and tan. We know the values of the trigonometric functions (sin, cos , tan, cot, sec, cosec) for the angles like 0°, 30°, 45°, 60°, and 90° from the trigonometric table. But to know the exact values of sin 22.5°, tan 15°, etc,… Continue reading Half Angle Formulas?

Sin 3x = 3sin x – 4sin3x Cos 3x = 4cos3x-3cos x T a n   3 x = 3   t a n   x − t a n 3 x / 1 − 3 t a n 2 x

The sum formula of tangent function is, tan (A + B) = (tan A + tan B) / (1 – tan A tan B) When A = B, the above formula becomes, tan (A + A) = (tan A + tan A) / (1 – tan A tan A) =(2 tan A) / (1 – tan2A)… Continue reading Double Angle Formulas of Tan

The sum formula of cosine function is, cos (A + B) = cos A cos B – sin A sin B When A = B, the above formula becomes, cos (A + A) = cos A cos A – sin A sin A cos 2A = cos2A – sin2A Let us use this as a… Continue reading Double Angle Formulas of Cos

The sum formula of sine function is, sin (A + B) = sin A cos B + cos A sin B When A = B, the above formula becomes, sin (A + A) = sin A cos A + cos A sin A sin 2A = 2 sin A cos A Let us derive an alternate… Continue reading Double Angle Formulas of Sin

sin(x+y) = sin(x)cos(y)+cos(x)sin(y) cos(x+y) = cos(x)cos(y)–sin(x)sin(y) t a n ( x + y ) = t a n   x + t a n   y / 1 − t a n   x . t a n   y sin(x–y) = sin(x)cos(y)–cos(x)sin(y) cos(x–y) = cos(x)cos(y) + sin(x)sin(y) t a n ( x − y ) = t a n   x − t a… Continue reading Sum and Difference Identities

The co-function or periodic identities can also be represented in degrees as: sin(90°−x) = cos x cos(90°−x) = sin x tan(90°−x) = cot x cot(90°−x) = tan x sec(90°−x) = cosec x cosec(90°−x) = sec x

These formulas are used to shift the angles by π/2, π, 2π, etc. They are also called co-function identities. sin (π/2 – A) = cos A & cos (π/2 – A) = sin A sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A sin (3π/2 – A)  =… Continue reading Periodicity Identities (in Radians)