Category: Trigonometry Formulas

sin2θ+cos2θ=1sin2⁡θ+cos2⁡θ=1 cot2θ+1=cosec2θcot2⁡θ+1=cosec2θ 1+tan2θ=sec2θ

sin-1 (–x) = – sin-1 x cos-1 (–x) = π – cos-1 x tan-1 (–x) = – tan-1 x cosec-1 (–x) = – cosec-1 x sec-1 (–x) = π – sec-1 x cot-1 (–x) = π – cot-1 x

We can prove these sum to product formulas using the product to sum formulas in trigonometry. The sum to product formula are expressed as follows: sin A + sin B = 2 sin [(A + B)/2] cos [(A – B)/2] sin A – sin B = 2 sin [(A – B)/2] cos [(A + B)/2] cos A…

We know that tan (A/2) = [sin (A/2)] / [cos (A/2)] From the half angle formulas of sin and cos, tan (A/2) = [±√(1 – cos A)/2] / [±√(1 + cos A)/2] = ±√[(1 – cos A) / (1 + cos A)] This is one of the formulas of tan (A/2). Let us derive the other two…

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…