Question

How to calculate the value of tan18 degree

Answer 1

Answer:

0.32491969623

Step-by-step explanation:

⋆  Let θ=18°

⟹5θ=900

⋆ Now, remember this identity :-

tan(θ1+θ2+…+θn)=S1−S3+S5−…1−S2+S4−…

where,

S1 = Sum of terms taken 1 at a time

S2 = Sum of terms taken 2 at a time

S3 = Sum of terms taken 3 at a time and so on…

**The terms are tanθ1,tanθ2,……tanθn

⋆ Let us write 5θ=θ+θ+θ+θ+θ :-

⟹tan5θ=tan(θ+θ+θ+θ+θ)=S1−S3+S51−S2+S4

⋆ Now, notice that :-

tan5θ=tan90o=∞

So, we can say that the denominator will be 0 i.e,

⟹1−S2+S4=0

⟹1–10tan2θ+5tan4θ=0

⋆ Let us take tan2θ=x :-

⟹5x2–10x+1=0

⟹x=1+25–√ [Rejected as tanθ<1⟹tan2θ<1]

⟹OR,x=1−25–√

⟹tanθ=tan18o=x−−√=1−25–√−−−−−−√=0.32491969623