The value of tan (π/8) is equal to

Question

The value of tan (π/8) is equal to (A) (1/2) (B) √2 + 1  (C) (1/√2 + 1)  (D) 1 - √2

Tardigrade Admin · Accepted Answer

We know that, tan θ=( sin 2 θ/1+ cos 2 θ) ⇒ tan (π/8)=( sin 2(π / 8)/1+ cos 2(π / 8)) ⇒ tan (π/8)=( sin (π / 4)/1+ cos (π / 4)) ∴ tan (π/8)=((1/√2)/1+(1)√2) =(1/√2+1)

Q. The value of $tan \frac{π}{8}$ is equal to

$\frac{1}{2}$

$2 + 1$

$\frac{1}{2 + 1}$

$1 - 2$

We know that, $tan θ = \frac{s i n 2 θ}{1 + c o s 2 θ}$
$\Rightarrow tan \frac{π}{8} = \frac{s i n 2 ( π /8 )}{1 + c o s 2 ( π /8 )}$
$\Rightarrow tan \frac{π}{8} = \frac{s i n ( π /4 )}{1 + c o s ( π /4 )}$
$∴ tan \frac{π}{8} = \frac{\frac{1}{2}}{1 + \frac{1}{2}}$
$= \frac{1}{2 + 1}$

Q. The value of tan8π​ is equal to

21​

2​+1

2​+11​

1−2​