Question

Розв‘яжіть тригонометричне рівняння ДЕТАЛЬНО! БЕЗ ФОТОМЕС.

cos4x-sin3x = 0

Answer 1

$\displaystyle\bf\\Cos4x-Sin3x=0\\\\Cos4x=Sin3x\\\\Cos4x=Cos\Big(\frac{\pi }{2} -3x\Big)\\\\\\4x=2\pi n\pm \Big(\frac{\pi }{2}-3x\Big)\\\\\\\left[\begin{array}{ccc}4x=2\pi n+\dfrac{\pi }{2}-3x \\4x=2\pi n-\dfrac{\pi }{2}+3x \end{array}\right\\\\\\\left[\begin{array}{ccc}7x=2\pi n+\dfrac{\pi }{2} \\x=2\pi n-\dfrac{\pi }{2} \end{array}\right\\\\\\\left[\begin{array}{ccc}x=\dfrac{2\pi n}{7}+\dfrac{\pi }{14} \\x=\dfrac{\pi }{2}(4n-1) \end{array}\right$

$\displaystyle\bf\\\left[\begin{array}{ccc}x=\dfrac{\pi }{14} (4n+1) \ ;n\in Z \\x=\dfrac{\pi }{2}(4n-1) \ ; \ n\in Z \end{array}\right$