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