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Question
Show that : tan 10° tan 15° tan 75° tan 80° = 1
Solution
L.H.S. = tan 10° tan 15° tan 75° tan 80°
= tan(90° – 80°) tan(90° – 75°) tan 75° tan 80°
= cot 80° cot 75° tan 75° tan 80° ...[∵ tan(90° – θ] = cot θ]]
= tan 80° cot 80° × tan 75° cot 75°
= 1 × 1
= 1 = R.H.S. ...(∵ tan A cot A = 1)
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