Match each expression in List I with its value in List II. List I List II (P) b 2 sin2C+ c 2 sin2B. (A) 1/ 6 (Q) B=60°,C=45°; D divides BC in ratio BD:DC=1:3. Find sin ∠ B A D /sin ∠ C A D . (B) 1 (

Question

Match each expression in List I with its value in List II. List I List II (P) b 2 sin2C+ c 2 sin2B. (A) 1/ 6 ​ (Q) B=60°,C=45°; D divides BC in ratio BD:DC=1:3. Find sin ∠ B A D /sin ∠ C A D . (B) 1 (R) C=90° and a≠b. Find [( a 2 + b 2 )/( a 2 - b 2 )]sin(A-B). (C) 2 (S) C=45°. Find (1+cot A)(1+cot B). (D) 4 Δ

TestHub · Accepted Answer

P equals abc/R=4 Δ . The sine rule and cevian area ratios give Q=(1/3)(sin B/sin C)=1/ 6 ​ . In R, sin(A-B)=( a 2 - b 2 )/ c 2 and c 2 = a 2 + b 2 , so R=1. The cotangent addition identity gives S=2.

Mathematics - Properties of Triangle Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(P) $b^{2}$ sin2C+ $c^{2}$ sin2B.	(A) 1/ $6$
(Q) B=60°,C=45°; D divides BC in ratio BD:DC=1:3. Find sin $∠ B A D$ /sin $∠ C A D$ .	(B) 1
(R) C=90° and a≠b. Find [( $a^{2}$ + $b^{2}$ )/( $a^{2}$ - $b^{2}$ )]sin(A-B).	(C) 2
(S) C=45°. Find (1+cot A)(1+cot B).	(D) 4 $Δ$