Question

tan (45° + 0). tan (45°- 0) FIQ=​

Answer 1

Answer:

tan 45 . tan 45 = tan ^2 45 = 1

adding or sustracting 0 will make no difference

so no need to overthink it

Answer 2

Answer:

tan(45+A)+tan(45-A) =

= [tan(45)+tanA] / [1-tan45.tanA] + [tan(45)-tanA] / [1+tan45.tanA] =

= (1+tanA) / (1-tanA) + (1-tanA) / (1 + tanA) =

= (1+tanA)^2 / (1-tan^2A) + (1-tanA)^2 / (1 - tan^2A) =

= [(1+tanA)^2 + (1-tanA)^2] / (1-tan^2A) = 2(1+tan^2A) / (1-tan^2A) =

= 2sec2A