समीकरण `sin 7theta + sin 5theta - cos 2theta =1` का व्यापक हल ज्ञात कीजिए |

Explanation

`sin 7theta + sin 5theta - cos 2theta =1`
`rArr " " 2 sin 6theta.cos theta -(2cos^(2)theta-1)=1`
`rArr " " 2 sin 6theta.cos theta -2 cos^(2)theta =0`
`rArr " " 2 cos theta (sin 6theta - cos theta) =0`
यदि `" " cos theta = 0 = "cos"(pi)/(2)rArr theta = (2n + 1)(pi)/(2)`.
यदि `" " sin 6theta - cos theta = 0 rArr sin 6theta = cos theta`
`rArr " " sin 6theta = sin((pi)/(2)-theta), therefore 6 theta = n pi = (-1)^(n)((pi)/(2)-theta)`
यदि n सम हो, तो `" " 6 theta = n pi + (pi)/(2)-theta`
`rArr " " 7theta = n pi + (pi)/(2)`
`rArr " " theta = (n+(1)/(2))(pi)/(7)`.
यदि n विषम हो, तो `" " 6 theta = n pi -(pi)/(2)-theta`
`rArr " " 5 theta = n pi -(pi)/(2)rArr theta = (n-(1)/(2))(pi)/(5)`.