"একটি সমকোণী ত্রিভুজে `ABC`, `C` তে সমকোণ, যদি `tanA=1` হয়, তাহলে যাচাই করুন যে `2sinAcosA=1`৷"

()123 $1. In a triangle ABC, a, b and c are the sides of the triangle satisfying the relation r1 + r2 = r3-r then the perimeter of the triangle 2ab a +b-c ab a +c-b ab a-b-c bc b+c-a 62. In ?ABC, which is not right angled, if p = sinA sinB sinc and q = cosA cosB cosc. Then the equation having roots tanA, tanB and tanC is (1) qxs_px® + (1+4)x-p=0 (2) qx3 + 2px" + qx-p=0 (3) qxs_ px2 + (2 + q)x + pq = 0 (4) qxs_px2 + qx + p = 0

If in a triangle ABC, (tanA)/1= (tanB)/2 = (tanC)/3 then prove that 6sqrt(2a)=3sqrt(5b)=2sqrt(10)c

Directions: In the question given below a statements is followed by three courses of action numbered I or (A), II or (B) and III or (C). A course of action is a step or administrative decision to be taken for improvement, follow-up for further action in regards to the problem, policy etc. on the basis of the information given in the statement. you have to assume everything in the statement to be true, then decide which of the three given/suggested courses of action logically follows for pursuing and decide the answer. Statements: 1. The company 'X' has rejected first lot of valves supplied by Company 'A' and has cancelled its entire huge order quoting use of inferior quality material and poor craftsmanship. Course of action: I. The Company 'A' needs to investigate functioning of its purchase, production and quality control departments. II. The Company 'A' should inspect all the valves rejected by Company 'X' . III. The Company 'A' should inform Company 'X' that steps have been taken for improvement and renegotiate schedule of supply. 1) Only I and II 2) Only II 3) All I, II and III 4)II and either I or III 5) None of these

Statement-1: In a !ABC , (a+b+c)(tanA/2+tanB/2)=2c cotC/2 Statement-2: In a !ABC , a = b cos C + c cos B

If A,B,C are the angles of a given triangle ABC . If cosA.cosB.cosC= (sqrt3-1)/8 and sinA.sinB.sinC= (3+sqrt3)/8 The value of tanA+tanB+tanC is (A) (3+sqrt(3)/(sqrt(3)-1)) (B) (sqrt(3)+4/(sqrt(3)-1)) (C) (6-sqrt(3)/(sqrt(3)-1)) (D) (sqrt(3)+sqrt(2)/(sqrt(3)-1))

Statement-1: In an acute angled triangle minimum value of tan alpha + tanbeta + tan gamma is 3sqrt(3) . And Statement-2: If a,b,c are three positive real numbers then (a+b+c)/3 ge sqrt(abc) into in a triangleABC , tanA+ tanB + tanC= tanA. tanB.tanC

If A,B,C are the angles of a given triangle ABC . If cosA.cosB.cosC= (sqrt3-1)/8 and sinA.sinB.sinC= (3+sqrt3)/8 The cubic equation whose roots are tanA, tanB, tanC is (A) x^3-(3+2sqrt(3))x^2+(5+4sqrt(3))x-(3+2sqrt(3))=0 (B) x^3-(3+-2sqrt(3))x^2+(5+4sqrt(3))x+(3+2sqrt(3))=0 (C) x^3+(3+2sqrt(3))x^2+(5+4sqrt(3))x+(3+2sqrt(3))=0 (D) x^3-(3+2sqrt(3))x^2+(5+4sqrt(3))x+(3+2sqrt(3))=0

65.Which one of the following statement is incorrect.(1) sino+sin 30+ sin 50+....+ sin(2n - 1) = SIEsine(11) The minimum value of sin^x+cos^x is(11) In an acute-angle tringle ABC, tanA tans tancs 313.(IV) tan6^@ tan42^@ tan 66^@ tan 78^@ =1(C) (111)(A) (1)(B) (11)(D) (M)