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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