Question

If sin(2x + 7)degrees =cos(4x-7)degrees, what is the value of x?

Answer 1

Answer:

x = 15

Step-by-step explanation:

$cosx = sin(\frac{\pi}{2} - x)$

$sin x = sin y = > x = sin^{-1}(sin y) = y => x = y$

$sin(2x + 7)^{\circ} = cos(4x - 7)^{\circ}\\\\sin(2x + 7)^{\circ} = sin(\frac{\pi}{2} - (4x - 7))\\\\(2x + 7) = (\frac{\pi}{2}- (4x -7))\\\\2x + 7 = \frac{\pi}{2} - 4x + 7\\\\6x = \frac{\pi}{2}\\\\x = \frac{\pi}{12}$

x = 15