Question

If an angle a is divided into two parts A and B such that A-B=x and TanA:Tan B=K:1
then Sinx=​

Answer 1

Answer:

(K - 1 / K + 1)Sinθ

Step-by-step explanation:

A - B = x (given)

A+B = θ (given because θ is divided into two parts)

TanA/TanB = K/1  (given)

=> TanA = KTanB.

=> SinA/CosA /SinB/CosB = K/1

=> SinACosB/CosASInB = K/1

Using compendo and dividendo rule

SinACosB + CosASinB/SinACosB - CosASinB =  K + 1 / K - 1

//Sin(A-B) = SinACosB - CosASinB and Sin (A+B) =  SinACosB + CosASinB

Sin(A+B)/Sin(A-B) = K + 1 / K - 1

Sinθ/Sinx = K + 1/K - 1

Sinx = (K - 1 / K + 1)Sinθ