Author: misamaliraza94

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) /…

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,…

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)…

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…

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…

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…

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)  =…