Question

Tan10° Tan20° Tan80° Tan70°=1

Answer 1

Step-by-step explanation:

tan10° × tan20° × tan80° × tan70° = 1

LHS = tan10° × tan80° × tan20° × tan70°

= tan10° × tan(90-10)° × tan20°× tan(90-20)°

= tan10° × cot10° × tan20° × cot20°

$= \tan(10°) \times \frac{1}{ \tan(10°) } \times \tan(20°) \times \frac{1}{ \tan(20°) }$

= 1

= RHS

Hence proved