Given equation ‌√6−5‌cos‌x+7sin‌2x−cos‌x=0 ⇒√6−5‌cos‌x+7−7cos2x−cos‌x=0 ⇒√13−5‌cos‌x−7cos2x−cos‌x=0 Squaring both sides, we get ‌⇒13−5‌cos‌x−7cos2x=cos2x ‌⇒13−5‌cos‌x−8cos2x=0 ‌⇒8cos2x+5‌cos‌x+13=0 Let y=cos‌x ⇒8y2+5y−13=0 ‌y=‌
−5±√25−4(8)(−13)
2×8
=‌‌
−5±√25+416
16
=‌
−5±21
16
⇒y=‌
−5+21
16
‌ or ‌y=‌
−5−21
16
⇒y=1‌ or ‌y=−‌
26
16
=−‌
13
8
(‌ not possible ‌) ∴‌‌cos‌x=1⇒cos‌x=1 And sin‌2x=1−cos2x=0⇒sin‌x=0 So, tan‌x=‌