Question

if tanA=√2+1 then tanA/1+tan^2A​

Answer 1

Answer:

[√2 - 1 ] / 2

Step-by-step explanation:

TanA = √2 + 1

1 + Tan²A = 1 + (√2 + 1)² = 1 + 2 + 1 + 2√2 = 4 + 2√2 = 2( 2 + √2)

TanA/ 1 + Tan²A = √2 + 1/ 2(2 + √2)

Multiply numerator and denominator by (2-√2) to simplify

                           = (√2 + 1)(2-√2)/2(2+√2)((2-√2)

                            = 2√2 + 2 - 2 - √2 / 2 (4 - 2)

                            = 2(√2 - 1) / 2 * 2

                             = [√2 - 1 ] / 2