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Dear Anil
1. Using the identity: tan x * tan(60° - x) * tan(60° + x) = tan(3x) well have for x = 5°:tan 5° tan 55° tan 65° = tan 15° = cot 75° = 1/tan 75°, hencetan 5° tan 55° tan 65° tan 75° = 1 ortan 5° = 1/(tan 55° tan 65° tan 75°) = cot 55° cot 65° cot 75° == tan 35° tan 25° tan 15°, so the answer is t = 5°Proof of the identity: tan x * tan(60° - x) * tan(60° + x) =(sin x * sin(60° - x) * sin(60° + x)) / (cos x * cos(60° - x) * cos(60° + x)) == (sin x * (cos 2x + 1/2)) / (cos x * (cos 2x - 1/2)) == ((1/2)(sin 3x - sin x) + (1/2) sin x) / ((1/2)(cos 3x + cos x) - (1/2) cos x) = tan 3x
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