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Find the exact value of coses 10^(@)+"co...

Find the exact value of coses `10^(@)+"coses"50^(@)-"cosec"70^(@)`

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The correct Answer is:
6
`(1)/( sin 10^(@)) + (1)/( sin 50^(@)) - (1)/( sin 70^(@))`
`" " = (1)/( cos 80^(@)) + (1)/( cos 40^(@)) - (1)/( cos 20^(@))`
`" " = (cos 40^(@) cos 20^(@) + cos 80^(@) cos 20^(@) - cos 40^(@) cos 80^(@))/( cos 20^(@) cos 40^(@) cos 80^(@))`
`= 8[ cos 20^(@) (cos 40^(@) + cos 80^(@)) - cos 40^(@) cos 80^(@)]`
` " "=8[ 2cos 20^(@) cos 60^(@) cos 20^(@) - cos 40^(@) cos 80^(@)]`
`= 4[2 cos ^(2) 20^(@) - 2 cos 40^(@) cos 80^(@)]`
` = 4 [ 1+ cos 40^(@) - ( cos 120^(@) + cos 40^(@))]`
`= 4xx (3)/(2) =6`
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