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
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<btn type=“success”>Question 1(v, vi, vii & viii) ></btn>