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 \(\rm \frac{6}{\cos x}-\frac{5}{\cos y}+8\tan y\) is:

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 4)

Answer 1

Given:

AD ⊥ BC ; ∠D = 90°

AC = 26 units; CD = 10 units; BC = 42 units

∠DAC = x and ∠B = y

Formula used:

Pythagorean theorem:

H² = P² + B²

Cos θ = B/H ; tan θ = P/B

Where, H = hypotenuse; P = perpendicular; B = Base

Calculation:

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

⇒ AB2 = 242 + 322

⇒ AB2 = 576 + 1024

⇒ AB = √1600 = 40 units

From the question:

\(\rm \frac{6}{\cos x}-\frac{5}{\cos y}+8\tan y\)

⇒ 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

∴ The correct answer is 25/4 units.

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