Question

Prove that tan10°. tan20°. tan30°. tan40°. tan50°. tan60°, tan 70°. tan80º = 1​

Answer 1

☯ To Prove,

• tan10°. tan20°. tan30°. tan40°. tan50°. tan60°, tan 70°. tan80° = 1

☯ Formula to be used,

• tan(90 - θ)° = Cotθ

☯ Solution,

LHS

tan10°. tan20°. tan30°. tan40°. tan50°. tan60°, tan 70°. tan80°

⇒ tan10° . tan20° . tan30° . tan40° . tan(90 - 50)° . tan(90 - 60)° . tan(90 - 70)° . tan(90 - 80)°

⇒ tan10° . tan20° . tan30° . tan40° . cot40°. cot30°. cot20° . cot10°

{ °.° Cancel out all }

⇒ 1

RHS

• Hence, Proved!!

Answer 2

tan10°. tan20°. tan30°. tan40°. tan50°. tan60°, tan 70°. tan80º

we know that tan (90−θ)= cotθ

= tan10∘.tan20∘.tan30∘.tan40∘.cot40∘.cot30∘.cot20∘.cot10∘

=1...........Use tan(90o−θ)=cotθ and tanθcotθ=1

= LHS = RHS

Hence , Verified .