If `xsin^(2)60^(@)-(3)/(2)sec60^(@)" "tan^(2)30^(@)+(4)/(5)sin^(2)45^(@)tan^(@)60^(@)=0` then x is

Options

A. `-(1)/(15)`
B. `-4`
C. `-(4)/(15)`
D. `-2`

Answer

c

Explanation

`x sin^(2)60-(3)/(2)sec60^(@)tan^(2)3 0^(@)`
`+(4)/(5)sin^(2)45^(@) tan^(2)60=0`
`rArrx((sqrt(3))/(2))^(2)-(3)/(2)xx2-((1)/sqrt(3))^(2)+(4)/(5)((1)/sqrt(2))^(2)`
`=(sqrt(3))^(2)=0`
`rArr(3x)/(4)-(3)/(2)xx2xx(1)/(2)xx3=0`
`rArr(3x)/(4)- 1+(6)/(5)=0`
`rArr(3x)/(4)=1-(6)/(5)rArr(5-6)/(5)=(-1)/(5)`
`x=-(1)/(5)xx(4)/(3)=-(4)/(15)`