Question

Sin5a+cos4a=2 find the number of solutions

Answer 1

$let \: \: a = \sin(5a) \\ \: \: \: \: \: \: \: b = \cos(4a) \\ given \: a + b = 2 \\ a \: or \: b < 1\: then \: b \: or \: a > 1 \: which \: is \: not \: possible \\ so \: \sin(5a) = 1 \: \: and \: \: \cos(4a) = 1 \\ 5a = n\pi + {( - 1)}^{n} \frac{\pi}{2} \: \: \: \: \: \: \: 4a = 2n\pi + - (0)\\ a = \frac{n\pi}{5} + {( - 1)}^{n} \frac{\pi}{2} \: \: \: \: or\: \: \: \: a = \frac{n\pi}{2}$
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