Question

What is the value of “x”?

Answer 1

29

Explanation:

`\sin \: (x - 3) = \cos \: (2x + 6) \\ \\ \sin \: (x - 3) = \sin \bigg \{ (\pi)/(2) - \: (2x + 6) \bigg\} \\ \\ x - 3 = ( \pi)/(2) - \: (2x + 6) \\ \\ x - 3 + 2x + 6 = (\pi)/(2) \\ \\ 3x + 3 = (\pi)/(2) \\ \\ 3x = (\pi)/(2) - 3 \\ \\ x = ((\pi)/(2) - 3 )/(3) \\ \\ x = (\pi)/(2 * 3) - (3)/(3) \\ \\ x = (\pi)/(6) - (3)/(3) \\ \\ x = 30 - 1 \\ \\ \huge \red{ \boxed{x = 29}} \\`