Question

What is the value of tan 22.5​

Answer 1

Explanation:

Call tan (22.5) = tan t --> tan 2t = tan 45 = 1

Use trig identity:

tan

2

t

=

2

tan

t

1

−

tan

2

t

(1)

tan

2

t

=

1

=

2

tan

t

1

−

tan

2

t

-->

-->

tan

2

t

+

2

(

tan

t

)

−

1

=

0

Solve this quadratic equation for tan t.

D

=

d

2

=

b

2

−

4

a

c

=

4

+

4

=

8

-->

d

=

±

2

√

2

There are 2 real roots:

tan t = -b/2a +- d/2a = -2/1 + 2sqrt2/2 = - 1 +- sqrt2

Answer:

tan

t

=

tan

(

22.5

)

=

−

1

±

√

2

Since tan 22.5 is positive, then take the positive answer:

tan (22.5) = - 1 + sqrt2

Answer 2

Answer:

hi,

root 2 -1

is your answer