Question

find the value of tan π/8.​

Answer 1

Answer:

Step-by-step explanation:

value of tanπ/8;

tan π/8=π/8×180 °/π

=tan(22.5°)

i.e tan(45°/2)

tan(A/2)=1-cosA/sinA

So,

tan(45 degree/2) =  1-cos(45 °/2)÷sin(45°/2)

 

cos 45°  =  1/√2

sin 45°   =   1/√2

1-cos(45 °/2)÷sin(45°/2)   =  1-1/√2÷1/√2

multiplying by √2 in numerator and denominaor

1-cos(45 °/2)÷sin(45°/2)  =  (1-1/√2)*√2÷(1/√2)*√2  

√2–1 Ans