Question

What is the value of tan18 degree

Answer 1

Hello....

▶Let θ = 18°.

so...

▶5θ = 90°

∴ 2θ + 3θ = 90°

⇒ 2θ = 90° – 30°

⇒ sin 2θ = sin (90° – 3θ) = cos 3θ

⇒ 2 sin θ cos θ = 4 cos3θ – 3 cos θ

⇒ 2 sin θ cos θ – 4 cos3θ + 3 cos θ = 0

⇒ cos θ (2 sin θ – 4 cos2 θ + 3) = 0

⇒ 2 sin θ – 4 (1 – sin2θ) + 3 = 0                            
<(cos θ = cos 18° ≠ 0)>

⇒ 4sin2 θ + 2 sin θ – 1 = 0

⇒ sinθ= ±(whole root)√2^2-4X4X-1

simplifying...

⇒ sin 18=√5-1/4

⇒  cos 18° = 1 − sin^2X18°

⇒ <whole root>√=1 − (5√−1)216

⇒ <whole root>√=16 − (5 + 1 − 25√)16

⇒ <whole root>√=16−(6−25√)16

⇒ <whole root>√=16 − 6 + 25√16

⇒ <whole root>√=10+25√16

⇒ <whole root>√=10+25√√4...

⇒ Now, tan 18° = sin 18°/cos 18° 

= √5 − 1/4 X4<whole root>√10+25

=▶▶√5 − 1/<whole root>10+25◀◀..

simplifying ⇒0.329......



thank you....

Answer 2

Answer:

Notice, we know  sin18∘=5√−14  &  cos18∘=10+25√√4  

∴tan18∘  

=sin18∘cos18∘  

=5√−1410+25√√4  

=5√−110+25√√  

=(5√−1)10−25√√10+25√√10−25√√  

=(10−25√)(5√−1)2√102−(25√)2√  

=(10−25√)(6−25√)√80√  

=80−325√√80√  

=80−325√√80√  

=$\sqrt{5-2\sqrt{5} ]/ 5$