Question

Prove that tan10°. tan20°. tan30°. tan40°. tan50°. tan60°. tan70°. tan80° = 1.


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Answer 1

Answer:

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!!

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

tan (90-80).tan (90-70).tan(90-30).tan(90-50). tan50.tan60.tan70.tan80

=cot80.cot70.cot60.cot50.tan50.tan60.tan70.tan80

=1 { tan×cot= 1, incase of same angles!}