Question
Without using trigonometric table, evaluate:
$
\cos 90^{\circ}+\sin 30^{\circ} \tan 45^{\circ} \cos ^2 45^{\circ}
$
$
\cos 90^{\circ}+\sin 30^{\circ} \tan 45^{\circ} \cos ^2 45^{\circ}
$
✓
Answer
$
\begin{aligned}
& \cos 90^{\circ}+\sin 30^{\circ} \tan 45^{\circ} \cos ^2 45^{\circ} \\
& \Rightarrow \cos 90^{\circ}+\sin 30^{\circ} \cdot \frac{\sin 45^{\circ}}{\cos 45^{\circ}} \cdot \cos ^2 45^{\circ} \\
& \Rightarrow \cos 90^{\circ}+\sin 30^{\circ} \cdot \sin 45^{\circ} \cdot \cos 45^{\circ} \\
& \Rightarrow 0+\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}
\end{aligned}
$
\begin{aligned}
& \cos 90^{\circ}+\sin 30^{\circ} \tan 45^{\circ} \cos ^2 45^{\circ} \\
& \Rightarrow \cos 90^{\circ}+\sin 30^{\circ} \cdot \frac{\sin 45^{\circ}}{\cos 45^{\circ}} \cdot \cos ^2 45^{\circ} \\
& \Rightarrow \cos 90^{\circ}+\sin 30^{\circ} \cdot \sin 45^{\circ} \cdot \cos 45^{\circ} \\
& \Rightarrow 0+\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}
\end{aligned}
$
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