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Question

The value of cosec10+cosec50cosec70 is

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Solution

cosec10+cosec50cosec70
=1sin10+1sin501sin70
=2sin50sin70+2sin10sin702sin10sin502sin10sin50sin70
=2sin70(sin50+sin10)2sin10sin502sin10sin(6010)sin(60+10)
=2sin70(2sin30cos20)cos40+cos602sin10sin(6010)sin(60+10)
=2sin270cos40+122sin10(sin260sin210)
=1cos140cos40+122(3sin104sin3104)
=cos40cos40+32sin302
=3214=6

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