Match the following. List-I List-II (a) If Δ = a 2 − ( b − c ) 2 , where Δ is the area of the triangle ABC, then tan A is equal to (p) 2 1 (b) In a Δ ABC, given that tan A : tan B : tan C = 3 : 4 :

Question

Match the following. List-I List-II (a) If Δ = a 2 − ( b − c ) 2 , where Δ is the area of the triangle ABC, then tan A is equal to (p) 2 1 ​ (b) In a Δ ABC, given that tan A : tan B : tan C = 3 : 4 : 5 , then the value of sin A sin B sin C is (q) 15 8 ​ (c) Let f ( θ ) = 2 cos 2 θ 1 − sin 2 θ + cos 2 θ ​ and α + β = 4 5 π ​ , then the value of f ( α ) f ( β ) is (r) 4 π ​ (d) The sum of the infinite terms of the series tan − 1 3 1 ​ + tan − 1 9 2 ​ + tan − 1 33 4 ​ + … is equal to (s) 7 2 5 ​ ​

TestHub · Accepted Answer

(a) Δ = a 2 − b 2 − c 2 + 2 b c ⇒ 2 b c cos A = 2 b c − Δ = 2 b c − 2 1 ​ b c sin A ⇒ 4 cos A + sin A = 4 ⇒ tan 2 A ​ = 4 1 ​ ⇒ tan A = 15 8 ​ (q). (b) tan A + tan B + tan C = tan A tan B tan C ⇒ 12 k = 60 k 3 ⇒ k = 5 ​ 1 ​ , so tan A = 5 ​ 3 ​ , tan B = 5 ​ 4 ​ , tan C = 5 ​ and sin A sin B sin C = 14 ​ 3 ​ ⋅ 21 ​ 4 ​ ⋅ 6 ​ 5 ​ ​ = 7 2 5 ​ ​ (s).

List-I	List-II
(a) If $Δ = a^{2} - (b - c)^{2}$ , where $Δ$ is the area of the triangle ABC, then $tan A$ is equal to	(p) $\frac{1}{2}$
(b) In a $Δ$ ABC, given that $tan A : tan B : tan C = 3 : 4 : 5$ , then the value of $sin A sin B sin C$ is	(q) $\frac{8}{15}$
(c) Let $f (θ) = \frac{1 - sin 2 θ + cos 2 θ}{2 cos 2 θ}$ and $α + β = \frac{5 π}{4}$ , then the value of $f (α) f (β)$ is	(r) $\frac{π}{4}$
(d) The sum of the infinite terms of the series $tan^{- 1} \frac{1}{3} + tan^{- 1} \frac{2}{9} + tan^{- 1} \frac{4}{33} + \dots$ is equal to	(s) $\frac{2 5}{7}$

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

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