` tan theta + tan 3 theta = 2 tan 2 theta ` से ` theta ` का व्यापक मान ज्ञात कीजिए ।

Explanation

` tan theta + tan 3 theta = 2 tan 2 theta `
` rArr (sin theta )/costheta+ (sin 3theta)/(cos 3theta)= (2sin 2theta)/(cos 2theta)`
` rArr (sin theta cos theta 3theta + sin cos theta )/(cos 3theta cos theta ) = (2sin 2theta)/(cos 2theta)`
` rArr (sin (theta+3theta))/(cos 3theta cos theta)= (2sin 2theta)/(cos2theta)`
` rArr sin 4 theta cos 2theta =2 sin 2theta cos 3theta cos theta `
` rArr 2sin 2theta cos 2theta cos 2theta cos 2theta - 2 sin 2theta cos 3theta costheta =0 `
` rArr sin theta [ 2 cos^(2) 2theta - 2 cos 3theta cos theta] =0`
` rArr sin 2theta[(1+ cos 4theta) - (cos 4theta + cos 2theta) = 0`
` rArr sin 2 theta ( 1- cos 2theta) =0`
` rArr sin 2 theta =0 "या " 1- cos 2theta = 0 `
अब ` sin 2theta = 0`
` 2 theta = n pi`
` rArr theta = (npi)/2 `
और ` 1- cos 2theta = 0 `
` rArr cos 2 theta = cos 0 `
` rArr 2 theta = 2n npi +0 `
` rArr theta = npi` ` rArr theta = npi`