Question

In the given figure, AD is perpendicular to BC. Find: 
`(3)/("sin"  x) + (4)/("cos"  y) - 4 "tan"  y`

Answer 1

ΔADB is a right-angled triangle.
∴ AB²
= AB² + BD²
= 12² + 16²
= 144 + 256
= 400
⇒ AB = 20cm
ΔADC is a right-angled triangle.
∴ AC²
= AD² + DC²
= 12² + 9²
= 144 + 81
= 225
⇒ AC = 15cm

`(3)/("sin"  x) + (4)/("cos"  y) - 4 "tan"  y`

= `(3)/("AD"/"AB") + (4)/("AD"/"AC") - 4 xx "CD"/"AD"`

= `(3)/(12/20) + (4)/(12/15) - 4 xx (9)/(12)`

= `(60)/(12) + (60)/(12) - 3`
= 5 + 5 - 3
= 7.