61. What is the value of A ? A -		cos θ	+	sin(-θ)	-	tan(90° + θ)		?
    		sin(90° + θ)		sin(180° + θ)		cot θ

    
    

1. 1. 1
      

   
   
   

   2. 2
      

   
   
   

   3. 3
      

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   	cos θ	+	sin(-θ)	-	tan(90° + θ)
   	sin(90° + θ)		sin(180° + θ)		cot θ

   
   

   =	cos θ	+		- sinθ		+	cotθ
   	cosθ			- sinθ			cot θ

   
   = 1 + 1 + 1 = 3

   Correct Option: C

   	cos θ	+	sin(-θ)	-	tan(90° + θ)
   	sin(90° + θ)		sin(180° + θ)		cot θ

   
   

   =	cos θ	+		- sinθ		+	cotθ
   	cosθ			- sinθ			cot θ

   
   = 1 + 1 + 1 = 3

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62. What is the value of tan		π	+ x		?
    		4

    
    

1. 1. 1 - tanx
      1 + tanx

      
      

   
   
   

   2. 1 + tanx
      1 - tanx

   
   
   

   3. 1 + cotx
      1 - cotx

   
   
   

   4. 1 - cotx
      1 + cotx

   
   
   

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1. View Hint View Answer Discuss in Forum

   tan					=	tan	π	+ tan x
   		π	+ x				4
   		4				1 - tan	π	tan x
   							4

   
   

   	∵ tan(A + b)	tanA + tanB
   		1 - tanA tanB

   
   

   =	1 + tanx
   	1 - tanx

   Correct Option: B

   tan					=	tan	π	+ tan x
   		π	+ x				4
   		4				1 - tan	π	tan x
   							4

   
   

   	∵ tan(A + b)	tanA + tanB
   		1 - tanA tanB

   
   

   =	1 + tanx
   	1 - tanx

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63. If cosC – cosD = y, then the value of y is
    

1. 1. 2sin		C + D		.sin		C - D
      		2				2

   
   
   

   2. 2cos		C + D		.cos		C - D
      		2				2

   
   
   

   3. - 2sin		C + D		.sin		C - D
      		2				2

   
   
   

   4. - 2cos		C + D		.cos		C - D
      		2				2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here,
   cosC – cosD = y
   ⇒ y = cosC – cosD
   ⇒ y = –2sin
   

   	C + D		.sin		C - D
   	2				2

   
   [∵ It is the basic formula of cosC – cosD]

   Correct Option: C

   Here,
   cosC – cosD = y
   ⇒ y = cosC – cosD
   ⇒ y = –2sin
   

   	C + D		.sin		C - D
   	2				2

   
   [∵ It is the basic formula of cosC – cosD]

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64. If sinx = 1/3 , then the value of sin3x will be
    

1. 1. 13
      27

   
   
   

   2. 27
      23

   
   
   

   3. 27
      13

   
   
   

   4. 23
      27

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here,
   

   sinx =	1
   	3

   
   We know that, sin3x = 3sinx – 4sin³x
   On putting the value of sinx, we get
   

   sin 3x = 3		1		- 4		1		³
   		3				3

   
   

   = 1 –	4
   	27

   
   

   =	27 - 4
   	27

   
   

   sin3x =	23
   	27

   Correct Option: D

   Here,
   

   sinx =	1
   	3

   
   We know that, sin3x = 3sinx – 4sin³x
   On putting the value of sinx, we get
   

   sin 3x = 3		1		- 4		1		³
   		3				3

   
   

   = 1 –	4
   	27

   
   

   =	27 - 4
   	27

   
   

   sin3x =	23
   	27

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65. If sinx × cosy + cosx × siny = 1, then the value of x + y will be
    

1. 1. π
      2

   
   
   

   2. -	π
      	2

   
   
   

   3. π
      3

   
   
   

   4. π
      4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here,
   sinx × cosy + cosx × siny = 1
   → sin(x + y) = 1
   [∵ sin (A + B) = sinA cosB + cosA sinB]
   

   ⇒ sin(x + y) = sin	π
   	2

   
   

   ⇒ x + y =	π
   	2

   Correct Option: A

   Here,
   sinx × cosy + cosx × siny = 1
   → sin(x + y) = 1
   [∵ sin (A + B) = sinA cosB + cosA sinB]
   

   ⇒ sin(x + y) = sin	π
   	2

   
   

   ⇒ x + y =	π
   	2

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