In a triangle ABC, a - 2b + c = 0. The value of cotA2cotC2&n

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 Multiple Choice QuestionsMultiple Choice Questions

51.

Angle α is divided into two parts A and B such that A - B = x and tan A : tan B = p : q. The value of sin(x) is equal to :

  • p + qsinαp - q

  • psinαp + q

  • psinαp - q

  • p - qsinαp + q


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52.

In a triangle ABC, a - 2b + c = 0. The value of cotA2cotC2 is  :

  • 92

  • 3

  • 32

  • 1


B.

3

a + c = 2b= cotA2cotC2= ss - as - bs - c × ss - cs - as - b= ss - b = 2s2s - 2b = a + b +ca + b + c - 2b = 3bb = 3


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53.

1 + sinA = sinA2 + cosA2 is true if :

  • 3π2 < A < 5π2 only

  • π2 < A < 3π2 only

  • 3π2 < A < 7π2

  • 0 < A < 3π2


54.

In triangle ABC, if sin2A + sin2B + sin2Ccos2A + cos2B + cos2C = 2 then the triangle is :

  • right angled

  • equilateral

  • isosceles

  • obtuse-angled


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55.

Given that tanα and tanβ are the roots of the equation. x2 + bx + c = 0 with b 0. What is tanα + β = ?

  • b(c - 1)

  • c(b - 1)

  • c(b - 1) - 1

  • b(c - 1) - 1


56.

Given that tanα and tanβ are the roots of the equation

x2 + bx + c = 0 with b  0

What is sinα + βsecαsecβ = ?

  • b

  •  - b

  • c

  •  - c


57.

Consider a triangle ABC in which

cosA + cosB + cosC = 3sinπ3

What is the value of sinA2sinB2sinC2 ?

  • 12

  • 14

  • 18

  • 116


58.

Consider a triangle ABC in which

cosA + cosB + cosC = 3sinπ3

What is the value of cosA + B2cosB + C2cosC + A2 ?

 

  • 14

  • 12

  • 116

  • None of the above


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59.

Consider the equation ksinx + cos2x = 2k - 7. If the equation possesses solution, then what is the maximum value of k ?

  • 1

  • 2

  • 4

  • 6


60.

Consider the following statements :

  1. If ABC is an equilateral triangle, then 3tan(A + B) tan (C) = 1
  2. If ABC is a triangle in which A = 78°, A = 66°, then tanA2 + C < tanA
  3. ABC is any triangle, then 

tanA +B2sinC2 < cosC2Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • 1 and 2

  • 2 and 3


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