Question

prove that tan181tan182tan183...tan268tan269=1

Answer 1

tan(180+x)=tanx

tan(90-x)=cotx

so

tan(180+1).tan(180+2).....tan(180+87).tan(180+88).tan(180+89)=

tan1.tan2.tan3........tan87.tan88.tan89=1

tan1.tan2.tan3.........tan(90-87).tan(90-88).tan(90-89)=1

tan1.tan2.tan3........cot3.cot2.cot1=1

tan1.tan2.tan3........1/tan3.1/tan2.1/tan1 =1 (cotx=1/tanx)

cut

tan1 with 1/tan1

so on

so we get

1.1.1........1.1.1=1

1=1

LHS=RHS

I HOP IT HELP U

THANKS