Question

if tan25 degree = a then prove that ,( tan 155 degree - tan 115 degree ) / ( 1+ tan 155 tan 115 degree ) = (1- a^2 ) /2a​

Answer 1

Answer:

Step-by-step explanation:

Use tan(180 - X) = -tanx

Hence tan155 = tan(180 - 25 ) =

-tan 25 = -a

tan(115) = tan(90 + 25) = -cot25 =

- 1/tan25 = -1/a

Now putting tan155 as -a and tan 115 as -1/a

We get (a - 1/a)/(a + 1/a)= 1 - a²/ 2a