56. What is the value of sin 240° ?
    

1. 1. √3

      2

   
   
   

   2. -	√3
      	2

   
   
   

   3. 1

      2

   
   
   

   4. -	1
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   sin 240° = sin(180° + 60°)
   = – sin 60° [∵ sin(180° + θ) = – sinθ]
   

   = -	√3
   	2

   Correct Option: B

   sin 240° = sin(180° + 60°)
   = – sin 60° [∵ sin(180° + θ) = – sinθ]
   

   = -	√3
   	2

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57. If cot (A + B) = x, then value of x is
    

1. 1. cotA.cotB – 1
      cotA + cotB

   
   
   

   2. cotA.cotB + 1
      cotA - cotB

   
   
   

   3. cotA.cotB – 1
      cotB - cotA

   
   
   

   4. cotA.cotB – 1
      cotA - cotB

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that,
   

   cot (A + B) =	cotA.cotB – 1
   	cotA + cotB

   
   

   ⇒ x =	cotA.cotB – 1
   	cotA + cotB

   Correct Option: A

   We know that,
   

   cot (A + B) =	cotA.cotB – 1
   	cotA + cotB

   
   

   ⇒ x =	cotA.cotB – 1
   	cotA + cotB

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58. What is the value of cos		7π		?
    		4

    
    

1. 1. 0
      

   
   
   

   2. 1
      

   
   
   

   3. 2
      

   
   
   

   4. 1/√2

   
   
   

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1. View Hint View Answer Discuss in Forum

   cos	7π	= cos		2π -	π		= cos	π
   	4				4			4

   
   ∵ cos (2π – θ) = cosθ
   

   =	1
   	√2

   Correct Option: D

   cos	7π	= cos		2π -	π		= cos	π
   	4				4			4

   
   ∵ cos (2π – θ) = cosθ
   

   =	1
   	√2

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59. What is the value of tan		5π		sin		7π		?
    		6				6

    
    

1. 1. 1
      √3

      
      

   
   
   

   2. 2
      √3

   
   
   

   3. 1
      2√3

   
   
   

   4. 1
      2

   
   
   

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1. View Hint View Answer Discuss in Forum

   tan		5π		.sin		7π
   		6				6

   
   

   = tan		π -	π		.sin		π +	π
   			6					6

   
   [∵ tan (180° – θ) = –tanθ sin (180° + θ) = –sinθ]
   

   = - tan	π		- sin	π
   	6			6

   
   

   = tan	π	× sin	π
   	6		6

   
   

   =	1	×	1
   	√3		2

   
   

   =	1
   	2√3

   Correct Option: C

   tan		5π		.sin		7π
   		6				6

   
   

   = tan		π -	π		.sin		π +	π
   			6					6

   
   [∵ tan (180° – θ) = –tanθ sin (180° + θ) = –sinθ]
   

   = - tan	π		- sin	π
   	6			6

   
   

   = tan	π	× sin	π
   	6		6

   
   

   =	1	×	1
   	√3		2

   
   

   =	1
   	2√3

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60. If sinx – cosx = 1, where ‘x’ is an acute angle, the value of (sinx + cosx) is :

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 1

      2

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   sinx – cosx = 1 ..... (i)
   sinx + cosx = y ..... (ii)
   On squaring and adding both equations,
   sin²x + cos²x – 2sinx.cosx + sin²x + cos²x + 2sinx . cosx
   = 1 + y²
   ⇒ 1 + 1 = 1 + y²
   ⇒ y² = 1 ⇒ y = 1

   Correct Option: B

   sinx – cosx = 1 ..... (i)
   sinx + cosx = y ..... (ii)
   On squaring and adding both equations,
   sin²x + cos²x – 2sinx.cosx + sin²x + cos²x + 2sinx . cosx
   = 1 + y²
   ⇒ 1 + 1 = 1 + y²
   ⇒ y² = 1 ⇒ y = 1

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