====== Question 1(ix, x & xi) Exercise 8.3 ======
Solutions of Question 1(ix, x & xi) of Exercise 8.3 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 1(ix)=====
Use the product-to-sum formula to change the sum or difference: $2 \sin 75{\circ} \sin 15{\circ}$.

** Solution. **

\begin{align*}
&\quad2 \sin 75^{\circ} \sin 15^{\circ} \\
&= \cos(75^{\circ} - 15^{\circ}) - \cos(75^{\circ} + 15^{\circ}) \\
&= \cos 60^{\circ} - \cos 90^{\circ} \\
\end{align*}
GOOD

=====Question 1(x)=====
Use the product-to-sum formula to change the sum or difference: $4 \sin \frac{u+v}{2} \cos \frac{u-v}{2} $.

** Solution. **

\begin{align*}
&4 \sin \frac{u+v}{2} \cos \frac{u-v}{2} \\
&= 2 \cdot 2 \sin \frac{u+v}{2} \cos \frac{u-v}{2} \\
&= 2[\sin\left( \frac{u+v}{2} + \frac{u-v}{2} \right) + \sin\left( \frac{u+v}{2} - \frac{u-v}{2} \right)] \\
&= 2[\sin u  + \sin v ]
\end{align*}
GOOD
=====Question 1(xi)=====
Use the product-to-sum formula to change the sum or difference: $2 \cos \frac{2u+2v}{2}\sin  \frac{2u-2v}{2} $.

** Solution. **

\begin{align*}
& 2 \cos \frac{2u+2v}{2}\sin  \frac{2u-2v}{2} \\
& = 2 \cos (u+v) \sin (u-v) \\
& = \sin \left(u+v+u-v \right) - \sin\left(u+v-u+v \right) \\
& = \sin 2u - \sin 2v 
\end{align*}
GOOD
====Go to ====

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