Question
In a $\triangle\text{ABC}$ right angled at B, $\angle\text{A}=\angle\text{C.}$ Find the values of.
$\sin\text{A}\cos\text{C}+\cos\text{A}\sin\text{C}$
$\sin\text{A}\cos\text{C}+\cos\text{A}\sin\text{C}$
✓
Answer
In $\triangle\text{le}\text{ ABC}\ \angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ $\angle\text{A}+90^\circ+\angle\text{A}=180^\circ$ $2\angle\text{A}=90^\circ$ $\angle\text{A}=45^\circ$$\therefore\ \angle\text{A}=45^\circ$
$\sin45^\circ\cos45^ \circ+\cos45^\circ\sin45^\circ$ $\frac{1}{\sqrt{2}}\cdot\frac{1}{\sqrt {2}}+\frac{1}{\sqrt{2}}\cdot\frac{1}{\sqrt {2}}=\frac{1}{2}+\frac{1}{2}=1$
$\sin45^\circ\cos45^ \circ+\cos45^\circ\sin45^\circ$ $\frac{1}{\sqrt{2}}\cdot\frac{1}{\sqrt {2}}+\frac{1}{\sqrt{2}}\cdot\frac{1}{\sqrt {2}}=\frac{1}{2}+\frac{1}{2}=1$
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