यदि `tan (alpha +theta)=n tan (alpha-theta)`, तो सिद्ध कीजिए की-
`(n+1) sin 2 theta=(n-1) sin 2 alpha`

Explanation

दिया है- `tan (alpha+theta)=n tan (alpha-theta)`
`implies (tan (alpha+theta))/(tan (alpha -theta))=n/1`
`implies (tan (alpha+theta)+tan (alpha-theta))/(tan (alpha+theta)-tan (alpha-theta))=(n+1)/(n-1)` (योगान्तरानुपात विधि से)
`implies ((sin (alpha+theta))/(cos (alpha+theta))+(sin (alpha-theta))/(cos (alpha-theta)))/((sin(alpha+theta))/(cos (alpha+theta))-(sin (alpha-theta))/(cos (alpha - theta)))=(n+1)/(n-1)`
`implies (sin (alpha+theta)cos (alpha -theta)+cos(alpha+theta) sin (alpha-theta))/(sin (alpha+theta)cos (alpha-theta)-cos(alpha+theta)sin(alpha-theta))=(n+1)/(n-1)`
`implies (sin (alpha+theta+alpha-theta))/(sin(alpha+theta-alpha+theta))=(n+1)/(n-1)`
`implies (sin 2 alpha)/(sin 2 theta)=(n+1)/(n-1)`
`implies (n-1) sin 2alpha=(n+1) sin 2 theta`
`implies (n+1) sin 2 theta=(n-1) sin 2 alpha`