Question
Sun May 06, 2012 By:

pls help me here

Expert Reply
Mon May 07, 2012
[{2/3 cosec^2 (58)} - {2/3 (cot 58)( tan 32)} - {5/3 (tan 13)( tan 37 )( tan 45 )( tan 53 )( tan 77)}]
Using: tan x = cot (90 - x)

={[2/3 cosec^2 58} -{2/3 cot^2 58} - {5/3 (tan 13 tan 37 tan 45 cot 37 cot 13}]
=2/3(cosec^2 58 - cot^2 58) - 5/3 [since, tan 45 = 1]
=2/3 -5/3 [Using cosec^2 x - cot^2 x = 1]
= -1
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