Question

prove tan 1° tan 10° Tan 20° tan70° tan80° tan89°= 1

Answer 1

tan 89 = cot (90-89) = cot 1

tan 80 = cot (90-80) = cot 10

tan 70 = cot (90-70) = cot 20

therefore tan 1 tan 10 tan 20 tan 70 tan80 tan 89= 1

since tan 89 × cot 1 = 1

there fore similrly all values become 1.