साबित करें कि `tan ((pi)/(4) + theta)+ tan((pi)/(4) - theta) = 2 sec 2theta `

Explanation

बायाँ पक्ष `= ( tan .(pi)/(4)+ tan theta)/(1-tan.(pi)/(4) tan theta) + ( tan . ( pi)/(4) - tan theta )/(1+tan . ( pi)/(4) tan theta)`
`= ( 1+ tan theta)/(1-tantheta)+ (1-tantheta)/(1+tan theta) = ((1+tan theta)^(2)(1-tantheta)^(2))/((1-tantheta)(1+tantheta))`
`= ((1+tan^(2)theta+2tan theta)+(1+tan^(2) theta-2 tan theta))/(1-tan^(2)theta)`
`= ( 2 ( 1+tan^(2)theta))/(1-tan^(2)theta)=(2)/(cos2theta)= 2 sec 2theta`