In the given figure, if AD⊥BC, AC = 26 units, CD = 10 units, BC = 42 units, ∠DAC = x and ∠B = y, then the value of $$\frac{6}{\cos x} - \frac{5}{\cos y} + 8 \tan y$$​ is:

Given: 

​$$AD\perp BC$$ , AC = 26 unit, CD = 10 unit,  BC = 42 unit

$$\angle DAC = x, \ \ \ \ \angle B = y$$ 

Concept Used: 

Pythagoras Theorem: 

​$$\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2$$ 

In △DAC,
AC² = AD² + CD²
26² = AD² + 10²
676 = AD² + 100
AD = √(676 - 100) = √576 = 24 units
In △ADB,
BD = (BC - CD) = (42 - 10) = 32 units
AB² = AD² + BD²
AB = √(24² + 32²)
AB² = 576 + 1024
AB = √1600 = 40 units
Given,
6 / (cos x) - 5 / (cos y) + 8tan y
= 6 / (AD / AC) - 5 / (BD / AB) + 8 × (AD / BD)
= 6 / (24 / 26) - 5 / (32 / 40) + 8 × (24 / 32)
= (6 × 26 / 24) - (5 × 40 / 32) + 8 × (24 / 32)
= 6.5 - 6.25 + 6
= 6.25 = 25/4 units ​​