Tiêu đề PROPERTIES OF TRIANGLES.pdf ✅

7. In a triangle ABC, √ s(s−a) bc = a) cos B 2 b) cos A 2 c) cos C 2 d) cos C JEE MAIN LEVEL - 1 SINGLE CORRECT CHOICE TYPE: 1. In △ ABC, if a = 4 cm, b = 7 cm, c = 9 cm, then tan A 2 = a) 1 √5 b) 1 √20 c) √20 d) 2 3 2. In △ ABC, if a = 5, s = 15, Δ = 30, then tan A 2 = a) 1 2 b) 3 2 c) 2 5 d) 1 5 3. In △ ABC, (a − b) 2 cos2 C 2 + (a + b) 2 sin2 C 2 = a) c b) c 2 c) 2c d) c 2 4. In △ ABC, bcos2 C 2 + ccos2 B 2 = a) s b) s-a c) s-b d) s − c 5. If the three sides of triangle are 5,7,8, then its area is (in sq. units) a) 10√3 b) 3√10 c) 3 √10 d) 10 √3 6. In △ ABC, if a, b, c are in A.P, then tan A 2 ,tan B 2 ,tan C 2 are in a) A.P b) G.P c) H.P d) A.G.P 7. In △ ABC, if a, b, c are in A.P, then cot A 2 , cot B 2 , cot C 2 are in a) A.P b) G.P c) H.P d) A.G.P INTEGER ANSWER TYPE: 8. If the sides a, b&c of △ ABC are in A.P, then acos2 C 2 + ccos2 A 2 = kb 2 , then k = JEE MAIN LEVEL - 2 9. In △ ABC, if 3a = b+ c, then cot B 2 ⋅ cot C 2 = a) 1 b) 2 c) 3 d) 4 10. sin ( A 2 +B) sin A 2 is always equal to a) b−c a b) b+c a c) b 2−c 2 a2 d) b 2+c 2 a2 11. In △ ABC, abccos A 2 cos B 2 cos C 2 = a) Δ 2 b) Δ 2 s 2 c) Δs d) s Δ2 12. In △ ABC, if (a + b + c)(b + c −a) = 3bc, then a) A = 60∘ b) B = 60∘ c) C = 60∘ d) A = 90∘ INTEGER ANSWER TYPE: 13. In △ ABC, if cos A + sin A − 2 cos B+sin B = 0, then the value of ( a+b c ) 4 is JEE MAIN LEVEL - 3 14. In △ ABC, if A = 3C, then a−c 2c = a) sin ( B 2 ) b) sin ( C 2 ) c) cos ( B 2 ) d) cos ( C 2 ) 15. In △ ABC, (a + b + c) (tan A 2 + tan B 2 ) = a) 2ccot A 2 b) 2ccot B 2 c) 2ccot C 2 d) 2ctan C 2 16. In △ ABC, 4Rcos A 2 cos B 2 cos C 2 = a) Δ b) s