# CAT Practice : Trigonometry

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Max and Min value of the given expression

## Trigonometry and Logarithm

Q.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°)
1. log √2/(1+√2)
2. -1
3. 1
4. none of these

Choice D. none of these

## Detailed Solution

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° + …….

=) As $cos (90 - \phi) = sin \phi : tan (90 - \phi) = cot \phi$

=) (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

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