Question

If `sin20^(@)=p, " then find the value of " ((sin380^(@)-sin340^(@))/(cos380^(@)+cos340^(@)))`.
A. `sqrt(1-P^(2))`
B. `sqrt((1-p^(2))/(p))`
C. `(p)/sqrt(1-p^(2))`
D. None of these

Answer 1

Correct Answer - C
Given, `sin20^(@)=p`
` sin380^(@)=sin(360^(@)+20^(@))`
`=sin 20^(@)`

`sin340^(@)=sin(360^(@)+20^(@))`
`=-sin20^(@)`
`cos380^(@)=cos(360^(@)+20^(@))`
`=cos20^(@)`
`cos340^(@)=cos(360^(@)-20^(@))`
`=cos20^(@)`
`therefore((sin380-sin340)/(cos380+cos340))=(sin20-(-sin20))/(cos20+cos20)`
`(2sin20)/(2cos20)`
`=tan20^(@)=(p)/(sqrt(1-p^(2)))`.