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Simplify : Tan 10° + tan 20°+tan 30°+tan 40° +tan50°+tan 60°+tan 70°+ Tan 80°

Simplify : Tan 10° + tan 20°+tan 30°+tan 40° +tan50°+tan 60°+tan 70°+ Tan 80°

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
I think there should not be any positive sign.
If it contains multiply sign between each term..then,
 
Tan 10 * tan 20 * tan30 * tan40 * tan 50 * tan 60 * tan70 * tan80
 
tan 10 * tan 20 * tan30 * tan 40 * tan(90-40) * tan (90-30) * tan (90-20)* tan (90-10)
tan 10 * tan 20 * tan 30 * tan 40 * cot 40 * cot 30* cot 20 * cot 10
 
Hence all canceks out and 
Answer is 1.
 
Regards
Arun (askIITians forum expert)

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