Question

Tan10°×tan20°×tan30°×......×tan70°×tan80°=??

Answer 1

Answer:

1

Step-by-step explanation:

tan10.tan20.tan30.tan40.tan50.tan60.tan70.tan80 (assuming 10, 20,30 etc given expressed in degree)

= tan10.tan20.tan30.tan40.tan(90–40).tan(90–30).tan(90–20). tan(90–10) ( 90=90°)

= tan10.tan20.tan30.tan40.cot40.cot30.cot20.cot10. { as tan(90-x)=cotx}

= tan10.cot10.tan20.cot20.tan30.cot30.tan40.cot40

= 1*1*1*1=1 (we know tanx.cotx=1)