Question

tan 18=?
Find ths value.​

Answer 1

Answer:

tan18=cot72....................

Answer 2

Answer:

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......

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