Question

solve the equation cos3x=sin2x​

Answer 1

Sometimes “degrees” are much friendlier than “radians”.

This is such a case.

If cos(3x) = sin(2x)

then cos(3x) = cos(90 – 2x)

so 3x = +90 – 2x + 360n or 3x = –(90 – 2x) + 360n

5x = 90 + 360n OR x = –90 + 360n

x = 18 + 72n OR x = –90 + 360n

x = 18, 90, 162, 234, 306, 376…. OR x = –90, 270, 630, 990….

Just as a check, the solutions are clearly represented on the graph of

y = cos(3x) – sin(2x).

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Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\tt{\rightarrow cos3x=cos(\dfrac{\pi}{2}-2x)}$

As we know that,

cos

$\tt{\rightarrow 3x=2n\pi \pm(\dfrac{\pi}{2}-2x)}$

$\tt{\rightarrow 3x=2n\pi+(\dfrac{\pi}{2}-2x)}$

$\tt{\rightarrow 3x=2n\pi-(\dfrac{\pi}{2}-2x)}$

$\tt{\rightarrow 5x=2n\pi+(\dfrac{\pi}{2})}$

$\tt{\rightarrow x=(2n\pi-\dfrac{\pi}{2})}$

$\tt{\rightarrow x=(\dfrac{2n\pi}{5}+\dfrac{\pi}{10})}$

$\tt{\rightarrow x=(2n\pi-\dfrac{\pi}{2})}$

Hence we get,

$\tt{\rightarrow x=(\dfrac{2n\pi}{5}+\dfrac{\pi}{10})}$

Or,

$\tt{\rightarrow x=(2n\pi-\dfrac{\pi}{2})}$