The value of ` (sin25^(@)cos65^(@)+cos25^(@)sin65^(@))/(tan^(2)70^(@)-co s ec^(2)20^(@))`

Options

A. `-1`
B. 0
C. 1
D. 2

Answer

a

Explanation

`(sin25^(@)cos65^(@)+cos25^(@)sin65^(@))/(tan^(2)70^(@)-co s ec^(2)20^(@))`
`=(sin25^(@)cos(90^(@)-25^(@))+cos25^(@) sin(90^(@)-25 ^(@)) )/(tan^(2)70^(@)-co s ec ^(2)20^(@))`
`=(sin^(2)25^(@)+cos^(2)25^(@))/(tan^(2)70^(@)-sec^(2)70^(@))`
`=(1)/(-1)=-1`