यदि (If) `cos theta = cos alpha . cos beta ` साबित करें कि
`tan. ( theta + alpha)/(2) tan . ( theta - alpha)/(2) = tan ^(2). ( beta)/(2)`

Explanation

प्रश्न से, `cos theta = cos alpha cos beta ` `:. cos beta = ( cos theta )/( cos alpha)` ….(1)
अब `tan^(2). (beta)/(2) = ( 1-cos beta)/( 1+ cos beta) = (1- (cos theta)/(cos alpha))/( 1+ ( cos theta )/( cos alpha)) = ( cos alpha - cos theta )/( cos alpha + cos theta )`
`= (2 sin . ( alpha+ theta)/(2) sin . ( theta- alpha)/( 2))/(2cos. ( theta+ alpha)/(2) cos . ( theta - alpha)/(2))= tan . ( theta + alpha )/(2) tan . ( theta - alpha)/( 2)`