In the following figure : AD ⊥ BC, AC = 26, CD = 10, BC = 42, ∠DAC = x and ∠B = y. Find the value of : (i) cot x (ii) 1/sin^2y - 1/tan^2y (iii) 6/cos x - 5/cos y + 8 tan y.

Question

In the following figure : AD ⊥ BC, AC = 26, CD = 10, BC = 42, ∠DAC = x and ∠B = y. Find the value of : (i) cot x (ii) 1/sin^2y - 1/tan^2y  (iii) 6/cos x - 5/cos y + 8 tan y.

KnowledgeBoat · Accepted Answer

Given, BC = 42 and CD = 10 From figure, BD = BC \- CD ⇒ BD = 42 \- 10 = 32 In Δ ACD, ⇒ AC2 = AD2 \+ CD2 (∵ AC is hypotenuse) ⇒ (26)2 = AD2 \+ (10)2 ⇒ 676 = AD2 \+ 100 ⇒ AD2 = 676 \- 100 ⇒ AD2 = 576 ⇒ AD = ⇒ AD = 24 In Δ ADB, ⇒ AB2 = AD2 \+ BD2 (∵ AB is hypotenuse) ⇒ AB2 = (24)2 \+ (32)2 ⇒ AB2 = 576 \+ 1,024 ⇒ AB2 = 1,600 ⇒ AB = ⇒ AB = 40 (i) cot (ii) sin tan Now, (iii) cos cos tan Now, Hence,

Mathematics

In the following figure : AD ⊥ BC, AC = 26, CD = 10, BC = 42, ∠DAC = x and ∠B = y. Find the value of : (i) cot x (ii) 1/sin^2y - 1/tan^2y (iii) 6/cos x - 5/cos y + 8 tan y.

Trigonometric Identities

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