Show that tan 10°.tan 20°. tan30°. tan40°. tan50°. tan 60°. tan7

1.	Show that tan 10°.tan 20°. tan30°. tan40°. tan50°. tan 60°. tan70°. tan80°= 1.
Answer» Answer: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 *= 1111=1 (we KNOW tanx.cotx=1)**

Show that tan 10°.tan 20°. tan30°. tan40°. tan50°. tan 60°. tan70°. tan80°= 1.

Answer»

Answer: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)