(iv) tan 15° tan 60° tan 75º = root 3
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tan 15° tan 25° tan 60° tan 65° tan 75° = cot(90° - 15°) tan (90° - 25°) tan 60° tan 65° tan 75° [∵ tan θ = cot (90° - θ)] = cot 75° cot 65° tan 60° tan 65° tan 75° = tan 60° [∵ tan 60° =√3] =√3 = RHSRead more on Sarthaks.com - https://www.sarthaks.com/929607/prove-that-tan15-tan25-tan60-tan65-tan75-3?show=929608#a929608
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hence prove65tan
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