यदि `sin theta = n sin ( theta + 2alpha)` तो सिद्ध करें कि
`tan ( theta + alpha) = (1+n)/(1-n) tan alpha`

Explanation

प्रश्न से, `sin theta = n sin ( theta + 2alpha ) ` या `(1)/(n) = ( sin (theta+2alpha))/(sin theta)`
या, `(1+n)/(1-n) = ( sin ( theta + 2alpha) + sin theta)/(sin ( theta+2alpha) - sin theta)`
`=( 2sin .(theta+2alpha+theta)/(2)cos.(theta+2alpha-theta)/(2))/(2cos.(theta+2alpha+theta)/(2)sin.(theta+2alpha-theta)/(2))=(2sin(theta+alpha)sinalpha)/(2cos(theta+alpha)sinalpha)`
`=tan(theta+alpha).cotalpha`
`=tan(theta+alpha)= (1+n)/(1-n)tanalpha`