Question

prove that tan 1*tan 89 + tan 2*tan 88 - tan 3*tan 87 - tan 4*tan 86 = 0

Answer 1

Answer:

tan1 = cot(90-1) =cot 89

tan 2= cot 90-2= cot 88

tan 3= cot 90-3 = cot 87

tan4=cot 90-4 =cot86

so putting the value we get

cot 89 tan89 + cot 88 tan 88 - cot 87 tan 87 -

cot 86 tan 86

we know that tanx*cotx=1

so

1+1-1-1=2-2

0 hence proved