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Advertisements advertisements question prove that 0 votes 5.6k views asked feb 10, 2022 in trigonometry by architakumari (42.5k points) closed feb 11, 2022 by architakumari prove the following Tan 20° tan 40° tan 60° tan 80° = 3 sum advertisements solution

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Prove that $ \tan 20°\cdot \tan 40° \cdot \tan 60° \cdot \tan 80° = 3$ [duplicate] ask question asked 9 years, 2 months ago modified 9 years, 2 months ago (i) tan 20^ (@) tan 40^ (@) tan 60^ (@) tan 80^ (@)=3 (ii) tan 20^ (@) tan 40^ (@) tan 80^ (@)=tan 60^ (@). To prove that \ ( \tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = 3 \), we will follow a systematic approach using trigonometric identities and properties.

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First, break tan 80 ∘ and tan 20 ∘ in terms of tan 60 ∘ and tan 20 ∘ by using a basic formula tan (a ± b) = tan a ± tan b 1 ∓ tan a tan b

After that multiply both the equations and simplify it Again, multiply by tan 20 ∘ and simplify it The equation will be in the form 3 tan a tan 3 a 1 3 tan 2 a which can be replaced by tan 3 a Now, the term tan 20 ∘ tan 40 ∘ tan.

Q.5 of chapter 8, prove that Tan 20° tan 40° tan 60° tan 80° = 3 Found 5 tutors discussing this question camila discussed prove that Tan 20° tan 40° tan 60° tan 80° = 3 7 mins ago discuss this question live

Trigonometric identities or values may now simplify specific terms further, but by evaluating directly, we find the approximate numerical value of this product

Through calculation or trigonometric tables Tan 20° × tan 40° × tan 60° × tan 80° = 3 Tan 20° × tan 40° × tan 60° × tan 80° = 3. Tan 20° tan 40° tan 60° tan 80° = 3 ← prev question next question → 0 votes 19.2k views

tan 20° tan 40° tan 60° tan 80° = tan 40° tan 80° tan 20° tan 60° = 2cos40ocos80ocos20o2sin40osin80osin20otan60o = 2cos40ocos80ocos20o2sin40osin80osin20o(3) = (cos40o+cos120o)cos20o(cos40o−cos120o)sin20o(3) = (2cos40o−1)cos20o(2cos40o+1)sin20o(3) = 2cos40ocos20o−cos20o2cos40osin20o+sin20o(3) = cos60o+cos20o−cos20osin60o−sin20o. We know that t a n θ t a n (60 o + θ) t a n (60 o − θ) = t a n 3 θ s o, ⇒ t a n 20 o t a n 80 o t a n 40 o t a n 60 o = t a n (20 0 × 3) × t a n 60 0 = 3 was this answer helpful? Evaluate without using trigonometric tables Tan 20.tan 40^ (@) tan 50^ (@) tan 70^ (@)

Sin 6θ - sin 2θ Prove that: cos 20° cos 40° cos 80° = 1 8 Prove that: 2 cos 𝜋 1 3 cos 9 𝜋 1 3 + cos 3 𝜋 1 3 + cos 5 𝜋 1 3 = 0 Evaluate: sin 50° - sin 70° + sin 10° If sin (y + z - x), sin (z + x - y), sin (x + y - z) are in A.P, then prove that tan x, tan y and tan z are in A.P.

Hence, we proved that the value of tan 20 o tan 40 o tan 60 o tan 80 o = 3 Here by looking at the terms like tan 20 o, tan 40 o and tan 60 o, students often make this mistake of using formulas of double angles that is tan 2 θ = 2 tan θ 1 tan 2 θ which makes the solution lengthy and does not lead to the desired result. S i n 3 𝐴 + s i n 5 𝐴 + s i n 7 𝐴 + s i n 9 𝐴 c o s 3 𝐴 + c o s 5 𝐴 + c o s 7 𝐴 + c o s 9 𝐴 = t a n 6 𝐴 prove that: Tan 20^@ tan 40^@ tan 60^@ tan 80^@=3.

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