Question

.Preove that tan 10: tan 75% tam 15 tan 80°=1​

Answer 1

Answer:

$identity \: used \\ tan(90 - x) = cotx \\ cotx \: = \frac{1}{tanx}$

$tan10 \: tan75 \: tan15 \: tan80 \\ = tan10 \: tan(90 - 15) \: tan15 \: tan(90 - 10) \\ = tan10 \: cot10 \: tan15 \: cot15 \\ = tan10 \: \frac{1}{tan10} \: tan15 \: \frac{1}{tan15} \\ = 1$