हल कीजिए - `tan theta + sec theta = 2 cos theta`

Explanation

दिया है - `tan theta + sec theta = 2cos theta `
`rArr (sin theta)/(cos theta) + 1/(cos theta) = 2 cos theta`
`rArr (sin theta+1)/(cos theta) = 2 cos theta`
`rArr 2 cos^(2) theta = 1 +sin theta`
`rArr 2 - 2 sin^(2) theta = 1 + sin theta`
`rArr 2 sin^(2) theta + 2 sin theta - sin theta -1 = 0`
`rArr (sin theta+1)(2 sin theta -1) = 0`
यदि `sin theta + 1 = 0 rArr sin theta = - 1 = sin. (3pi)/2`
` :. theta = n pi + (-1)^(n) . (3pi)/2 , n in Z`
जो कि स्वीकार्य नहीं है क्योंकि `pi/2` के विषम गुणज के लिए व परिभाषित नहीं है ।
यदि `2sin theta -1 = 0 rArr sin theta = 1/2 = sin . pi/6`
`:. theta = n pi + (-1)^(n) pi/6, n in Z`