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The smallest positive value of x (in deg...

The smallest positive value of x (in degrees) for whichcos `tanx=(cos5^@ cos 20^@ + cos 35^@ cos 50^@-sin 50^@ sin 20^@ - sin35^@ sin50^@)/(sin5^@ cos 20^@ - sin 35^@ cos 50^@ + cos 5^@ sin 20^@ - cos 35^@ sin 50^@)` is equal to

A

`-(1)/(sqrt(3))`

B

`(1)/(sqrt(3))`

C

`-sqrt(3)`

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(-sin 5^(@)sin20^(@)-sin 35^(@)sin 50^(@))/(sin 5^(@)cos 20^(@)-sin 35^(@)cos 50^(@))+ cos 5^(@) sin 20^(@)-cos 35^(@) sin 50^(@)`
`(cos 25^(@)+cos 15^(@))+(cos 85^(@)+cos 15^(@))`
`=(-(cos 15^(@)-cos 25^(@))-(cos 15^(@)-cos 85^(@)))/((sin 25^(@)-sin 15^(@))-(sin 85^(@)-sin 15^(@)))+(sin 25^(@)+sin 15^(@))-(sin 85^(@)+sin 15^(@))`
`=(cos 25^(@)+cos 85^(@))/(sin 25^(@)-sin 85^(@))`
`=-(2 cos 55^(@) cos 30^(@))/(2 cos 55^(@)sin 30^(@))`
`=-cot 30^(@)=-sqrt(3)`
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