101. If tan θ = 1, then the value of	8sin θ + 5cos θ	is
     	sin3θ - 2cos3θ + 7cos θ

1. 1. 2

   
   
   

   2. 2	1
      	2

   
   
   

   3. 3

   
   
   

   4. 	4
      	5

   
   
   

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   tanθ = 1
   ⇒ θ = 45°
   

   ∴	8 sin θ + 5 cos θ
   	sin3θ - 2cos3θ + 7 cosθ

   
   
   

   Correct Option: A

   tanθ = 1
   ⇒ θ = 45°
   

   ∴	8 sin θ + 5 cos θ
   	sin3θ - 2cos3θ + 7 cosθ

   
   
   

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102. If tan θ = 1, then the value of	8sin θ + 5cos θ	is
     	sin3θ - 2cos3θ + 7cos θ

1. 1. 2

   
   
   

   2. 2	1
      	2

   
   
   

   3. 3

   
   
   

   4. 	4
      	5

   
   
   

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1. View Hint View Answer Discuss in Forum

   tanθ = 1
   ⇒ θ = 45°
   

   ∴	8 sin θ + 5 cos θ
   	sin3θ - 2cos3θ + 7 cosθ

   
   
   

   Correct Option: A

   tanθ = 1
   ⇒ θ = 45°
   

   ∴	8 sin θ + 5 cos θ
   	sin3θ - 2cos3θ + 7 cosθ

   
   
   

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103. If sin α sec (30° + α) = 1 (0 < a < 60°), then the value of sin α + cos 2α is

1. 1. 1

   
   
   

   2. 	2+√3
      	2√3

   
   
   

   3. 0

   
   
   

   4. √2
      

   
   
   

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   	sinα	= 1
   	cos(30° + α)

   
   

   ⇒	sinα	= 1
   	sin(90° - 30 - α)

   
   

   ⇒	sinα	= 1
   	sin(60° - α)

   
   ⇒ sin α = sin (60° – α)
   ⇒ 2α = 60° ⇒ α = 30°
   ∴ sinα + cos 2α
   = sin 30° + cos 60°
   

   =		1	+	1	= 1
   		2		2

   
   

   Correct Option: A

   	sinα	= 1
   	cos(30° + α)

   
   

   ⇒	sinα	= 1
   	sin(90° - 30 - α)

   
   

   ⇒	sinα	= 1
   	sin(60° - α)

   
   ⇒ sin α = sin (60° – α)
   ⇒ 2α = 60° ⇒ α = 30°
   ∴ sinα + cos 2α
   = sin 30° + cos 60°
   

   =		1	+	1	= 1
   		2		2

   
   

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104. If cos⁴ θ – sin⁴ θ = (2 / 3) , then the value of 2 cos²θ– 1 is

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 	2
      	3

   
   
   

   4. 	3
      	2

   
   
   

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   cos4 θ - sin4 θ =	2
   	3

   
   

   (cos2 θ + sin2 θ) (cos2 θ – sin2 θ)	2
   	3

   
   

   ⇒ cos2 θ - sin2 θ	2
   	3

   
   

   ⇒ 2cos2 θ - 1	2
   	3

   
   

   Correct Option: C

   cos4 θ - sin4 θ =	2
   	3

   
   

   (cos2 θ + sin2 θ) (cos2 θ – sin2 θ)	2
   	3

   
   

   ⇒ cos2 θ - sin2 θ	2
   	3

   
   

   ⇒ 2cos2 θ - 1	2
   	3

   
   

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105. If sin α + cos β = 2 (0° ≤ β ≤ α ≤ 90°), then sin (2α + β / 3) =

1. 1. sin	α
      	2

   
   
   

   2. cos	α
      	3

   
   
   

   3. sin	α
      	3

   
   
   

   4. cos	2α
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   sinα + cosβ = 2
   sinα ≤ 1 ; cosβ ≤ 1
   ⇒ α = 90° ; β = 0°
   
   

   = sin 60° =	√3
   	2

   
   Also,
   

   cos		α	= cos 30° =	√3
   		3		2

   
   

   Correct Option: B

   sinα + cosβ = 2
   sinα ≤ 1 ; cosβ ≤ 1
   ⇒ α = 90° ; β = 0°
   
   

   = sin 60° =	√3
   	2

   
   Also,
   

   cos		α	= cos 30° =	√3
   		3		2

   
   

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