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.

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*}

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*}

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*}

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*}

Question 1(v, vi, vii & viii) >