Question

Prove that sin(theta+phi)/sin theta.cos phi= cot theta tan phi +1​

Answer 1

Prove that sin(x+y)/sin x.cos y= cotx tany+1​ (in better form)

Given:

sin(x+y)/sin x.cos y

To prove:

sin(x+y)/sin x.cos y= cotx tany+1

Proof:

Let us take the LHS of the given equation:

• sin(x+y)/sin x.cos y

We have the formula of

sin(x+y) = sin x.cos y + sin y.cos x

Putting this in the equation;

• sin x.cos y + sin y.cos x/sin x.cos y

Distribute the Denominator

• sin x.cos y/sin x.cos y + sin y.cos x/sin x.cos y
• 1+ sin y.cos x/cos y.sin x
• 1 + tany.cotx

sin(x+y)/sin x.cos y= cotx tany+1

Henve proved.