The question is from CAT Geometry - Trigonometry. This is about Trigonometry and Logarithm. We need to find out of the given expression which contains both logarithm and trigonometric ratio. Trigonometry is an important topic for CAT Preparation for the CAT Exam. Trigonometric ideas can be completely opposite, as in, some questions test lot of common sense with direction, heights and distances, while others could test you on identities. CAT exam could test one on both these fronts. Make sure you master both in CAT - Trigonometry.
Question 7: Find the value of :- (log sin 1° + log sin 2° ………..+ log sin 89°) + (log tan 1° + log tan 2° + ……… + log tan 89° ) - (log cos 1° + log cos 2° + ……… + log cos 89°)
Writing the equation as :-
(log sin 1° - log cos 89°) + (log sin 2° - log cos 88°) + (log sin 3° - log cos 87°)………… + log tan 1°. log tan 89° + log tan 2°. log tan 88° + …….
=> cos (90 - ∅) = sin∅ : tan (90 - ∅) = cot∅
=> (log sin 1° - log sin 1°) +(log sin 2° - log sin 2°)+……..+ log tan 1°cot 1° + log tan 2°cot 2°
=> log 1 = 0
The question is "Find the value of the above given term"
Choice D is the correct answer.
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