निम्नलिखित समीकरणों को हल कीजिए -
(i) `cot theta+tan theta = 2 cosec theta" "(ii) 7cos^(2) theta + 3 sin^(2) theta = 4`

Explanation

(i) दिया है - ` cot theta+tan theta = 2 cosec theta`
`rArr (cos theta)/(sin theta) +(sin theta)/(cos theta) = 2/(sin theta)`
`rArr cos^(2) theta + sin^(2) theta = 2 cos theta`
`rArr 1 = 2 cos theta`
`cos theta = 1/2 = cos . pi/3`
`:. theta = 2n pi pm pi/3, n in Z`
(ii) दिया है - `7cos^(2) theta + 3 sin^(2) theta = 4`
`rArr 7cos^(2) theta + 3 (1 -cos^(2) theta) = 4`
`rArr 7 cos^(2) theta +3 -3 cos^(2) theta = 4`
`rArr 4 cos^(2) theta = 1`
` cos theta = pm 1/2`
यदि `cos theta = + 12 rArr" " theta = 2 n pi pm pi/3`
और यदि `cos theta = - 1/2 rArr" " theta = 2 n pi pm (2pi)/3 , n in Z`