Question

find the value of tan 22.5°​

Answer 1

Refer to the attachment for your solution.

Answer 2

Answer:

Tan 22.5°  = √2 - 1

Step-by-step explanation:

Tan 2α  = 2Tanα /(1 - Tan²α)

α = 22.5 °

=> 2α = 2 * 22.5 = 45°

& Tan 45° = 1

Lets call Tan 22.5° = x

=> 1 = 2x/(1 - x²)

=> 1 - x² = 2x

=> x² + 2x - 1 = 0

=> x  = (- 2 ± √2² - 4(1)(-1) )/2

=> x = ( - 2 ± √8 )/2

=> x =  ( - 2 ± 2√2 )/2

=> x = - 1 ± √2

=> x = √2 - 1    or -1 - √2

as 22.5° lies in 1st Quadrant and is +ve

so  -1 - √2 will be ignored

Hence x =  √2 - 1

=> Tan 22.5°  = √2 - 1