Question

Langdon thinks that the sum sin30+sin30 is equal to sin60. Do you agree with Langdon? Explain what this means about the sum of the sines of angles.

Answer 1

Answer:

Langdon is not correct. It means distributive property is not applicable for sines of angles.

Step-by-step explanation:

According to Langdon

$\sin 30 +\sin 30=\sin 60$

We need to check whether Langdon is correct or not.

Taking LHS,

$LHS=\sin 30 +\sin 30$

$LHS=2\sin 30$

$LHS=2(\frac{1}{2})$            $[\because \sin 30=\frac{1}{2}]$

$LHS=1$

Taking RHS,

$RHS=\sin 60$

$RHS=\frac{\sqrt{3}}{2}$           $[\because \sin 60=\frac{\sqrt{3}}{2}]$

Since LHS ≠ RHS, therefore Langdon is not correct.

It means distributive property is not applicable for sines of angles.

$\sin A+\sin B\neq \sin (A+B)$