Question

find the value of tan π/8​

Answer 1

Answer:

45/2

Step-by-step explanation:

π=180

so,180/8=45/2(divide by 4 in numerator and denominator)

Answer 2

Answer:

√2 - 1

Step-by-step explanation:

tanπ/8 = tan (180/8) = tan 45/2

//now to find value of Tan 45/2, use Tan2x = 2 tanx/ 1-tan²x

Tan (2*45/2) = 2 tan 45/2 / 1 - tan²45/2

Tan45 = 2tan(45/2) / 1 - tan²45/2

1 = 2tan(45/2) / 1 - tan²45/2

=> 1 - tan²45/2 = 2tan45/2

=> tan²45/2 + 2tan45/2 - 1 = 0

//this looks like a quadratic equation of form ax² + bx + c so x can be found using x = -b±√b2-4ac/2a

=> a = 1, b = 2, c= -1

tan45/2 = -2±√4 - 4(1)(-1) / 2*1 =  [-2±2√2] / 2 = -1 ± √2.

=> tan 45/2 can be -1+√2 or -1 - √2.

But tan 45/2 cannot be -1 - √2 as 45/2° falls in first quadrant and thus its value cannot be negative.

So tan45/2 = √2 - 1.

=> Tan π/8 =  √2 - 1.