Home
Class 12
MATHS
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)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

  • VECTOR ALGEBRA

    CENGAGE|Exercise Solved Examples And Exercises|519 Videos

Similar Questions

Explore conceptually related problems

The smallest positive value of x (in degrees) for whichcos tan x=(cos5^(@)cos20^(@)+cos35^(@)cos50^(@)-sin50^(@)sin20^(@)-sin35^(@)sin50^(@))/(sin5^(@)cos20^(@)-sin35^(@)cos50^(@)+cos5^(@)sin20^(@)-cos35^(@)sin50^(@))

Find the least positive x in degree for which tan x= (cos5^(@)cos20^(@)+cos35^(@)cos50^(@)-sin5^(@)sin20^(@)-sin35^(@)sin50^(@))/(sin5^(@)cos20^(@)-sin35^(@)cos50^(@)+cos5^(@)sin20^(@)-cos35^(@)sin50^(@))

Find the least positive value of x in degrees for which tanx=(cos5^0cos20^0+cos35^0cos50^0-sin5^0sin20^0-sin35^0sin50^0)/(sin5^0cos20^0-sin35^0cos50^0+cos5^0sin20^0-cos35^0sin50^0)

Find the least positive x in degree for which tanx=(cos5^0cos20^0+cos35^0cos50^0-sin5^0sin20^0-sin35^0sin50^0)/(sin5^0cos20^0-sin35^0cos50^0+cos5^0sin20^0-cos35^0sin50^0)

If cos25^(0)+sin25^(0)=K, then cos50^(@) is equal to

cos (40^@ + theta) - sin (50^@ - theta) is equal to

(cos 70^(@))/(sin 20^(@)) + (cos 59^(@))/(sin 31^(@) ) - 8 sin^(2) 30^(@) is equal to