In the given figure, if AD⊥BC, AC = 26 units, CD = 10…

In the given figure, if AD⊥BC, AC = 26 units, CD = 10 units, BC= 42 units, ∠DAC = x and ∠B = y, then the value $\frac{6}{cosx}-\frac{5}{cosy}+8tany$

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{25}{4}$ units

Given that

if AD ⊥ BC, AC = 26 units, CD = 10 units, BC= 42 units, $\angle$ DAC = x and $\angle$ B = y

BD = BC - CD = 42 - 10 = 32 units

cos x = AD/AC, cos y = BD/AB

In triangle ACD

AD² = AC² - CD²

AD²= 26² - 10² = 676 - 100 = 576

AD = 24 units

Similarly, in triangle ADB

AB² = AD² + BD²

AB²= 24² + 32² = 1600

AB = 40 units

Thus, cos x = AD/AC = 24/26, cos y = BD/AB = 32/40, tan y = AD/BD = 24/32

Hence, the value of 6/cos x - 5/cos y + 8 tan y

= 6/(24/26) - 5/(32/40) + 8 × (24/32)

= 26/4 - 25/4 + 24/4 = 25/4 units

SSC CGL 2023 PYQ — Question 62