Question

Find the general solution of the equation
tane + tan 20 + tan 30 = tane tan 20 tan 30.​

Answer 1

Step-by-step explanation:

= 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)

Answer 2

Answer:

= 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)