## If three angles A, B and C are in A.P prove that CotB = (SinA – SinC)/(CosC – CosA)

As angles A, B and C are in A.P (Arithmetic Progression) therefore 2B = A + C, this is just a general rule for Arithmetic Progression series. Let’s now move onto simplifying right…

## Prove that (SinA + Sin3A + Sin5A + Sin7A)/(CosA + Cos3A + Cos5A + Cos7A) = Tan4A

Simplifying left hand side of equation (SinA + Sin3A + Sin5A + Sin7A)/(CosA + Cos3A + Cos5A + Cos7A) = Tan4A Using formulasSinC + SinD = 2 Sin(C + D)/2 Cos(C – D)/2…

## Prove that (Cos8A Cos5A – Cos12A Cos9A)/(Sin8A Cos5A + Cos12A Sin9A) = Tan4A

Let’s simplify left hand side of this equation (Cos8A Cos5A – Cos12A Cos9A)/(Sin8A Cos5A + Cos12A Sin9A) = Tan4A Multiplying and dividing by 2 Using formulas2 CosA CosB = Cos(A + B) +…

## Prove that SinA + Sin3A + Sin5A + Sin7A = 4 CosA Cos2A Sin4A

Let’s prove that SinA + Sin3A + Sin5A + Sin7A = 4 CosA Cos2A Sin4A Let’s simplify left hand side of this equationSinA + Sin3A + Sin5A + Sin7A (SinA + Sin3A) +…

## Prove that Cot4A (Sin5A + Sin3A) = CotA (Sin5A – Sin3A)

Simplifying Left Hand Side Cot4A (Sin5A + Sin3A) Cot4A (Sin5A + Sin3A) Using formulaSinC + SinD = 2 Sin(C + D)/2 Cos(C – D)/2 ReplacingC = 5AD = 3A (C + D)/2 =…

## Prove that (Sin3A + SinA) SinA + (Cos3A – CosA) CosA = 0

In this article, we will discuss how to prove that (Sin3A + SinA) SinA + (Cos3A – CosA) CosA = 0 Let’s simplify left hand side of this equation(Sin3A + SinA) SinA +…

## Prove that (Sin5A + Sin3A)/(Cos5A + Cos3A) = Tan4A

Let’s simplify (Sin5A + Sin3A) and (Cos5A + Cos3A) individually and then divide Simplifying (Sin5A + Sin3A) Using formula SinC + SinD = 2 Sin(C + D)/2 Cos(C – D)/2 ReplacingC = 5AD…