समीकरण `3tan (theta - 15^(@))=tan (theta + 15^(@))` को हल कीजिए |

Explanation

`because " " 3tan (theta - 15^(@))=tan (theta + 15^(@)) " "` [दिया है]
`rArr " " (tan (theta +15^(@)))/(tan(theta - 15^(@)))=3`
`rArr " " (sin(theta + 15^(@))cos (theta -15^(@)))/(sin(theta-15^(@))cos(theta+15^(@)))=(3)/(1)`
`rArr " " (sin 2theta + sin 30^(@))/(sin 2theta - sin 30^(@))=(3)/(1)`
`rArr " " (2sin 2theta)/(2sin 30^(@))=(3+1)/(3-1) " "` [योगान्तरानुपात से]
`rArr " " (sin 2theta)/(sin 30^(@))=2`
`rArr " " sin 2theta = 2 sin 30^(@)`
`rArr " " sin 2theta = 2 xx (1)/(2)=1- "sin"(pi)/(2)`
`rArr " " 2theta = npi + (-1)^(n)pi//2`, जहाँ `n in I`
अतः `theta` का अभीष्ट मान `= theta = (1)/(2)[n pi + (-1)^(n)(pi)/(2)]`, जहाँ `n in I`.