समीकरण `sin theta + sin 2theta + sin 3theta + sin 4theta =0` का व्यापक हल ज्ञात कीजिए |

Explanation

`sin theta + sin 2theta + sin 3theta + sin 4theta = 0`
`rArr " " (sin theta + sin 4theta)+(sin 2theta+sin 3theta)=0`
`rArr " 2 sin" (theta)/(2)"cos"(3theta)/(2)+"2 sin"(5theta)/(2)"cos"(theta)/(2)=0`
`rArr " sin"(5theta)/(2)("cos"(3theta)/(2)+"cos"(theta)/(2))=0`
`rArr " sin"(5theta)/(2)(2cos.theta cos theta//2)=0`
`therefore " sin"(5theta)/(2)=0, cos theta = 0` या `cos theta//2 =0`.
(i) यदि `"sin"(5theta)/(2)=0`, तो `"sin"(5theta)/(2)=sin 0`
`therefore" " (5theta)/(2)=n pi rArr theta = (2n pi)/(5)`, जहाँ `n in I`.
(ii) यदि `cos theta = 0`. तो `cos theta = cos pi//2`
`therefore " " theta = 2 n pi pm pi//2`, जहाँ `n in I`.
(iii) यदि `cos theta//2=0`, तो `cos theta//2=cos pi//2`
`therefore " " theta//2 = 2n pi pm pi//2`
`rArr " " ttheta = 4n pi pm pi`, जहाँ `n in I`.