Write the value of ^2 24^ - ^2 6^ . - Vidyadip

Question

Write the value of $\sin ^2 24^{\circ}-\sin ^2 6^{\circ}$.

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Answer

$\begin{array}{l}\Rightarrow \quad \sin ^2 24^{\circ}-\sin ^2 6^{\circ} \\ \Rightarrow \quad \sin \left(24^{\circ}+6^{\circ}\right) \sin \left(24^{\circ}-6^{\circ}\right) \\ \Rightarrow \quad \sin 30^{\circ} \sin 18^{\circ}=\frac{1}{2} \times\left(\frac{\sqrt{5}-1}{4}\right) \\ \Rightarrow \quad \frac{1}{8}(\sqrt{5}-1) \end{array}$

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