समीकरण ` tan theta - cot theta = "cosec" theta ` को हल कीजिए ।

Explanation

` tan theta - cot theta = "cosec" theta `
` rArr (sin theta)/(cos theta) - (cos theta)/(sin theta) = 1/(sin theta) `
` rArr (sin^(2) theta - cos ^(2) theta)/(cos theta sin theta ) = 1/(sin theta )`
` rArr sin^(2) - cos ^(2) theta = cos theta `
` rArr 1 - cos^(2) - cos^(2) theta = cos theta `
` rArr 2 cos^(2) theta + cos theta - 1 = 0 `
` rArr 2 cos^(2) theta + 2 cos theta - cos theta - 1 = 0 `
` rArr 2 cos theta ( cos theta +1) -1 (cos theta +1)=0`
` rArr ( cos theta +1) (2 cos theta -1) = 0 `
` rArr cos theta + 1 =0 " या " 2 cos theta -1 = 0 `
अब ` cos theta + 1 = 0 `
` rArr cos theta = - 1 = - cos pi `
` rArr theta = 2 npi pm pi `
और ` 2 cos theta - 1 = 0 `
` rArr cos theta = 1/2 = cos.pi/3`
` rArr cos theta = 1/2 = cos .pi/3 `
` rArr theta = 2npi pm pi/3 .`