Question

1/cos290+1/√3sin250=?

Answer 1

We have : cos 290° = cos (270°+20°) = sin 20° 

. . . . . . . . sin 250° = sin (270°-20°) = - cos 20°. 

∴ ( 1 / cos 290° ) + (1 / √3 sin 250° ) 

= ( 1 / sin 20° ) + { 1 / [ √3 ( - cos 20° ) ] } 

= ( √3 cos 20° - sin 20° ) / ( √3 sin 20° cos 20° ) 

= 2 [ (√3 /2 ) cos 20° - (1/2) sin 20° ] / [ (√3/2) ( 2 sin 40°] 

= 2 ( sin 60° cos 20° - cos 60° sin 20° ) / ((√3/2) sin 40° ) 

= 2 sin (60° - 20°) / ((√3 /2) sin 40° ) 

= 4 / √3