Question

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Answer 1

Step-by-step explanation:

$sin( \alpha + 30 \degree) = cos \alpha + sin( \alpha - 30 \degree) \\ RHS = cos \alpha + sin( \alpha - 30 \degree) \\ = cos \alpha + sin \alpha \: cos 30\degree - cos \alpha \: sin 30\degree \\ = cos \alpha - cos \alpha \: sin 30\degree + sin \alpha \: cos 30\degree \\ = cos \alpha (1- sin 30\degree) \: + sin \alpha \: cos 30\degree \\ = cos \alpha (1- \frac{1}{2} ) \: + sin \alpha \: cos 30\degree \\ = cos \alpha (\frac{1}{2} ) \: + sin \alpha \: cos 30\degree \\ = cos \alpha sin 30\degree \: + sin \alpha \: cos 30\degree \\ = sin( \alpha + 30 \degree) \\ = LHS \\ thus \: proved.$