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

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

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((1)/(2))`
`[\because \sin 30=(1)/(2)]`

`LHS=1`

Taking RHS,

`RHS=\sin 60`

`RHS=(√(3))/(2)`
`[\because \sin 60=(√(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\\eq \sin (A+B)`