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The value of $\frac{\sin 85^{\circ}-\sin 15^{\circ}}{\cos 65^{\circ}}=$
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Verified Answer
The correct answer is:
1
$\frac{\sin 85^{\circ}-\sin 35^{\circ}}{\cos 65^{\circ}}$
$\begin{aligned}
&=\frac{2 \cos \left(\frac{85^{\circ}+35^{\circ}}{2}\right) \sin \left(\frac{85^{\circ}-35^{\circ}}{2}\right)}{\cos 65^{\circ}} \\
&=\frac{2 \cos 60^{\circ} \sin 25^{\circ}}{\cos 65^{\circ}} \\
&=\frac{2 \times \frac{1}{2} \times \sin 25^{\circ}}{\cos \left(90^{\circ}-25^{\circ}\right)} \\
&=\frac{\sin 25^{\circ}}{\sin 25^{\circ}}=1
\end{aligned}$
$\begin{aligned}
&=\frac{2 \cos \left(\frac{85^{\circ}+35^{\circ}}{2}\right) \sin \left(\frac{85^{\circ}-35^{\circ}}{2}\right)}{\cos 65^{\circ}} \\
&=\frac{2 \cos 60^{\circ} \sin 25^{\circ}}{\cos 65^{\circ}} \\
&=\frac{2 \times \frac{1}{2} \times \sin 25^{\circ}}{\cos \left(90^{\circ}-25^{\circ}\right)} \\
&=\frac{\sin 25^{\circ}}{\sin 25^{\circ}}=1
\end{aligned}$
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