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TAN1.TAN2.TAN3.......................TAN89

TAN1.TAN2.TAN3.......................TAN89

Grade:11

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear Raj,

tan1.tan2.........tan89
but tan 89 can be written as cot 1[tan(90-1)=cot 1] by tan(90-theta)=cot(theta)
likewise......,
tan 88 =cot 2
tan 87= cot 3
................up to tan 46=cot 44
then middle one is tan 45 =1
so it is
tan1.tan2...........tan44.tan 45.cot44..............cot1
tan and cot cancel out by[tan (theta)*cot(theta)=1
so ....remaining is 1
answer =1

 

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