` tan ((pi)/4+theta/2)+tan((pi)/4-theta/2)` बराबर है

Options

A. `sec theta`
B. `2 sec theta`
C. ` sec. theta/2`
D. इनमे से कोई नहीं

Answer

B

Explanation

` tan ( pi/4+theta/2 ) + tan ( pi /4 - theta /2)`
` = ( 1 + tan. theta/2)/(1-tan. theta / 2) + ( 1 - tan. theta / 2 )/ ( 1 + tan. theta/2) = ((1+ tan theta //2)^(2) + (1- tan theta//2)^(2))/(1- tan^(2) theta//2)`
` = (2+ 2 tan^(2) theta//2)/(1- tan^(2) theta//2) = 2 ((1tan^(2) theta //2 )/(1- tan^(2) theta //2))`
` = 2 (1/(cos theta)) = 2 sec theta " " [ :' cos theta = (1-tan^(2). theta/2)/(1+ tan^(2). theta/2)]`