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Question

Without using trigonometric table, evaluate :
23cosec258o23cot58otan32o53tan13otan37otan45otan53otan77o

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Solution

23cosec258o23cot58otan32o53tan13otan37otan45otan53otan77o

=23cosec258o23cot58otan(90o58o)53tan13otan37otan45otan(90o37o)tan(90o13o)

=23cosec258o23cot258o53tan13otan37otan45ocot37ocot13o

=23(cosec258ocot258o)53tan13otan37o×1×1tan37o×1tan13o

=23×153=1

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