sin-pi-sin-x-cos-pi-sin-x-1-find-x-

Question Number 164511 by HongKing last updated on 18/Jan/22

\sin \cdot (π \sin x) - \cos \cdot (π \sin x) = 1

find x = ?

Answered by mindispower last updated on 18/Jan/22

s i n (a) - c o s (a) = \sqrt{2} s i n (a - \frac{π}{4})

\Leftrightarrow w i t h e a = π s i n (x)

s i n (a - \frac{π}{4}) = \frac{1}{\sqrt{2}}

\Leftrightarrow a - \frac{π}{4} = \frac{π}{4} + 2 k π, \frac{3 π}{4} + 2 k π

s i n (x) = 1 + 2 k \in {1, - 1}

x = \frac{π}{2} + k π

π s i n (x) = \frac{π}{2} + 2 k π

s i n (x) = \frac{1}{2} + 2 k, \Rightarrow k = 0

s i n (x) = \frac{1}{2}, x \in {\frac{π}{6} + 2 k π, \frac{5 π}{6} + 2 k π}

Commented by HongKing last updated on 20/Jan/22

thank you dear Sir cool