u want the product of these??

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u want the product of these??

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=sin1/cos1 .sin 2/cos 2 . ...sin 45/cos 45 .....sin 88/cos 88 . sin 89/ cos 89

=sin(90-89)/cos 1 . sin(90-88)/cos 2...........sin(90-45)/cos 45.........sin(90-1)/cos89

=cos 89/cos1 .cos 88/cos 2......cos 45/cos 45 ..........cos 1/ cos 89

all the values will get cancelled......and the result will be 1

Example:-

Let's take tan 89 and tan 1 in the first case and Let's take Tan 2 and tan 88 in 2nd case:-

=) tan(90-89) tan89

=) cot89 x tan89

=) 1/tan89 x tan89 [tan89 will be canceled on both the sides by multiplying]

=) 1. Ans.

=) tan(90-88) tan88

=) cot88 x tan88

=) 1/tan88 x tan88 [tan 88 will be canceled on both the sides by multiplying]

=) 1.Ans.

Therefore, if we go on doing this for every ratios...we will come to the answer 1 for each case.

Hence, Answer = 1.