## Prove that Cos18° – Sin18° = √2 Sin27°

Let’s simplify Cos18° – Sin18° Sin18° can be written as Sin(90° – 72°) = Cos72°Because Sin(90° – θ) = Cosθ for any angle θ Therefore Cos18° – Sin18° becomes Cos18° – Cos72° CosC…

## Show that Sin(B – C) Cos(A – D) + Sin(C – A) Cos(B – D) + Sin(A – B) Cos(C – D) = 0

Using Product to Sum Trigonometry formulasSinA CosB = 1/2 [Sin(A + B) + Sin(A – B)] Sin(B – C) Cos(A – D) = 1/2 [Sin(B – C + A – D) + Sin(B…

## Show that SinA Sin(B – C) + SinB Sin(C – A) + SinC Sin(A – B) = 0

Using Product to Sum Trigonometry formula SinA SinB = 1/2 [Cos(A – B) – Cos(A + B)] SinA Sin(B – C) = 1/2 [Cos(A – (B – C)) – Cos(A + B –…

## Prove that Sin25° Cos115° = 1/2 (Sin140° – 1)

Let’s simplify left hand side of equation Sin25° Cos115° = 1/2 (Sin140° – 1) Using formula SinA CosB = 1/2 [Sin(A + B) + Sin(A – B)] ReplacingA = 25°B = 115° Sin25°…

## Show that Sin50° Cos85° = (1 – √2 Sin35°)/2√2

Let’s simplify left hand side of equation Sin50° Cos85° = (1 – √2 Sin35°)/2√2 Using formula SinA CosB = 1/2 [Sin(A + B) + Sin(A – B)] ReplacingA = 50°B = 85° Sin50°…

## Prove that 2 Sin(5𝝅/12) Cos(𝝅/12) = (√3 + 2)/2

Let’s simplify left hand side of equation 2 Sin(5𝝅/12) Cos(𝝅/12) = (√3 + 2)/2 2 Sin(5𝝅/12) Cos(𝝅/12) Using formula 2 SinA CosB = Sin(A + B) + Sin(A – B) ReplacingA = 5𝝅/12B…

## Prove that 2 Cos(5𝝅/12) Cos(𝝅/12) = 1/2

Let’s simplify left hand side of equation 2 Cos(5𝝅/12) Cos(𝝅/12) = 1/2 Using formula 2 CosA CosB = Cos(A + B) + Cos(A – B) ReplacingA = 5𝝅/12B = 𝝅/12 2 Cos(5𝝅/12) Cos(𝝅/12)…

## Prove that 2 Sin(5𝝅/12) Sin(𝝅/12) = 1/2

Let’s simplify left hand side of equation 2 Sin(5𝝅/12) Sin(𝝅/12) = 1/2 Using formula 2 SinA SinB = Cos(A – B) – Cos(A + B) ReplacingA = 5𝝅/12B = 𝝅/12 2 Sin(5𝝅/12) Sin(𝝅/12)…

## Prove that 4 SinA Sin(𝝅/3 + A) Sin(2𝝅/3 + A) = Sin3A

This article discuss how to prove that 4 SinA Sin(𝝅/3 + A) Sin(2𝝅/3 + A) = Sin3A Let’s simplify left hand side and prove that its equal to right hand side value Sin3A…

## Prove that CosA Cos(𝝅/3 – A) Cos(𝝅/3 + A) = 1/4 Cos3A

This article discuss how to prove that CosA Cos(𝝅/3 – A) Cos(𝝅/3 + A) = 1/4 Cos3A Let’s simplify left hand side and prove that its equal to right hand side value 1/4…