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Question

The value of cos58sin32+sin22cos68cos38cosec 52tan18tan35tan72tan55
is

A
0
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B
12
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C
1
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D
2
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Solution

The correct option is C 1
cos58sin32+sin22cos68cos38cosec 52tan18tan35tan72tan55=cos(9032)sin32+sin(9068)cos68cos38cosec 52tan18tan35tan72tan55=1+1cos38cosec (9038)tan18tan35tan72tan55=21tan18tan35tan72tan55

Now,
tan18tan35tan72tan55=tan18tan35tan(9018)tan(9035)=tan18tan35cot18cot35=(tan18cot18)(tan35cot35)=1

Therefore,
cos58sin32+sin22cos68cos38cosec 52tan18tan35tan72tan55=21=1

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