====== Question 1(i, ii, iii & iv)  Exercise 8.3 ======
Solutions of Question 1(i, ii, iii & iv) 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(i)=====
Use the product-to-sum formula to change the sum or difference: 
$$4 \sin 16x \cos 10x $$

** Solution. **

\begin{align*}
&4 \sin 16x \cos 10x \\
& = 2 (2\sin 16x \cos 10x) \\
&= 2[\sin(16x+10x)+\sin(16x-10x)]\\
&= 2[\sin (26x)+\sin(6x)]
\end{align*}
GOOD
=====Question 1(ii)=====
Use the product-to-sum formula to change the sum or difference: $10 \cos 10y \cos 6y$.

** Solution. **

\begin{align*}
&10 \cos 10y \cos 6y \\
&= 5(2 \cos 10y \cos 6y) \\
&= 5[\cos(10y + 6y)+\cos(10y - 6y) ] \\
&= 5[\cos(16y)+\cos(4y)  ]
\end{align*}
GOOD
=====Question 1(iii)=====
Use the product-to-sum formula to change the sum or difference: $2 \cos5t \sin 3t$.

** Solution. **

\begin{document}
\begin{align*}
&2 \cos 5t \sin 3t \\
&= \sin(5t + 3t) - \sin(5t - 3t) \\
&= \sin(8t) - \sin(2t)
\end{align*}

=====Question 1(iv)=====
Use the product-to-sum formula to change the sum or difference: $6\cos 5x \sin 10x$.

** Solution. **

\begin{align*}
&6 \cos 5x \sin 10x \\
&= 3(2 \cos 5x \sin 10x) \\
&= 3[\sin(10x + 5x) - \sin(10x - 5x)] \\
&= 3[\sin(15x) - \sin(5x)]
\end{align*}
GOOD
====Go to ====

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