====== Question 3, Review Exercise ======
Solutions of Question 3 of Review Exercise of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 
=====Question 3(i)=====
Express as single trigonometric ratio: $\frac{1}{\sqrt{2}}(\sin \beta+\cos \beta)$\\
** Solution. **

\begin{align*}
&\frac{1}{\sqrt{2}}(\sin \beta+\cos \beta)\\
=& \sin \frac{\pi}{4}\sin \beta+\cos \frac{\pi}{4}\cos \beta\\
=& \cos(\beta -\frac{\pi}{4})
\end{align*}
 
=====Question 3(ii)=====
Express as single trigonometric ratio: $\frac{1}{\sqrt{2}} \sin 75^{\circ}+\frac{1}{\sqrt{2}} \cos 75^{\circ}$

** Solution. **

\begin{align}
&\frac{1}{\sqrt{2}} \sin 75^{\circ} + \frac{1}{\sqrt{2}} \cos 75^{\circ} \notag \\
=& \sin \frac{\pi}{4} \sin 75^{\circ} + \cos \frac{\pi}{4} \cos 75^{\circ} \notag \\
=& \cos\left(75^{\circ} - \frac{\pi}{4}\right)
\end{align}




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