Question
Prove the following:
$\cos^22\text{x}-\cos^26\text{x}=\sin8\text{x}\sin4\text{x}$
$\cos^22\text{x}-\cos^26\text{x}=\sin8\text{x}\sin4\text{x}$
$=(\cos2\text{x}+\cos6\text{x})(\cos2\text{x}-6\text{x})$
$=\Big[2\cos\Big(\frac{2\text{x}+6\text{x}}{2}\Big)\cos\Big(\frac{2\text{x}-6\text{x}}{2}\Big)\Big]\Big[-2\sin\Big(\frac{2\text{x}+6\text{x}}{2}\Big)\sin\Big(\frac{2\text{x}-6\text{x}}{2}\Big)\Big]$
$=[2\cos4\text{x}\cos(-2\text{x})][-2\sin4\text{x}\sin(-2\text{x})]$
$=[2\cos4\text{x}\cos2\text{x}][-2\sin4\text{x})(\sin-2\text{x})]$
$=(2\cos4\text{x}\cos4\text{x})(2\sin2\text{x}\cos2\text{x})$ $=\sin8\text{x}\sin4\text{x}$ $=\text{R.H.S.}$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Find the term independent of x in the expansion of the following expressions:
$\Big(\frac{3}{2}\text{x}^{2}-\frac{1}{3\text{x}}\Big)^{6}$