Trigonometry

Trigonometry

Easy Questions
Moderate Questions
Difficult Questions
Trigonometry Tutorial

Aptitude

Simplification
Number System
Fractions
Elementary Algebra
LCM and HCF
Approximation
Unitary Method
Linear Equation
Quadratic Equation
Discount
Average
Surds and Indices
Percentage
Square root and cube root
Order of Magnitude
Work and Wages
Odd Man Out and Series
Algebra
Profit and Loss
Stocks and Shares
True Discount
Ratio, Proportion
Partnership
Alligation or Mixture
Time and Work
Pipes and Cistern
Speed, Time and Distance
Problem on Trains
Height and Distance
Banker's Discount
Boats and Streams
Races and games
Problems on Ages
Clocks and Calendars
Simple interest
Compound Interest
Sets and Functions
Area and Perimeter
Volume and Surface Area of Solid Figures
Sequences and Series
Plane Geometry
Logarithm
Probability
Permutation and Combination
Statistics
Mensuration
Trigonometry
Aptitude miscellaneous
  1. If sin P + cosec P = 2, then the value of sin7P + cosec7P is








  1. View Hint View Answer Discuss in Forum

    sinP + cosec P = 2

    ⇒ sinP +
    1
    		 = 2
    sin P

    ⇒
    sin²P + 1
    		 = 2
    sin P

    ⇒ sin²P + 1 = 2 sinP
    ⇒ sin²P – 2sin P + 1 = 0
    ⇒ (sin P – 1)2 = 0
    ⇒ sinP – 1 = 0
    ⇒ sinP = 1
    ∴ cosec P = 1
    ∴ sin7P + cosec7P
    = 1 + 1 = 2

    Correct Option: B

    sinP + cosec P = 2

    ⇒ sinP +
    1
    		 = 2
    sin P

    ⇒
    sin²P + 1
    		 = 2
    sin P

    ⇒ sin²P + 1 = 2 sinP
    ⇒ sin²P – 2sin P + 1 = 0
    ⇒ (sin P – 1)2 = 0
    ⇒ sinP – 1 = 0
    ⇒ sinP = 1
    ∴ cosec P = 1
    ∴ sin7P + cosec7P
    = 1 + 1 = 2

  1. If sin A + sin²A =1 then what is the value of cos²A + cos4A ?








  1. View Hint View Answer Discuss in Forum

    sin A + sin²A = 1
    ⇒ sin A = 1 – sin²A = cos²A
    ∴ cos4A = sin²A
    ∴ cos²A + cos4A
    = cos²A + sin²A = 1

    Correct Option: B

    sin A + sin²A = 1
    ⇒ sin A = 1 – sin²A = cos²A
    ∴ cos4A = sin²A
    ∴ cos²A + cos4A
    = cos²A + sin²A = 1

  1. If sin (3x – 20°) = cos (3y + 20°), then find the value of (x + y).








  1. View Hint View Answer Discuss in Forum

    sin (3x – 20°) = cos (3y + 20°)
    ⇒ sin (3x – 20°)
    = sin {90° – (3y + 20°)}
    [∵ sin (90° – θ) = cosθ]
    ⇒ 3x – 20° = 90° – 3y – 20° = 70° – 3y
    ⇒ 3x + 3y = 70° + 20° = 90°
    ⇒ 3 (x + y) = 90°

    ⇒ x + y =
    90°
    		 = 30°
    3

    Correct Option: D

    sin (3x – 20°) = cos (3y + 20°)
    ⇒ sin (3x – 20°)
    = sin {90° – (3y + 20°)}
    [∵ sin (90° – θ) = cosθ]
    ⇒ 3x – 20° = 90° – 3y – 20° = 70° – 3y
    ⇒ 3x + 3y = 70° + 20° = 90°
    ⇒ 3 (x + y) = 90°

    ⇒ x + y =
    90°
    		 = 30°
    3

  1. If cosα/cosβ = m and cosα/sinβ = n, then the value of (m² + n²) cos²b is :








  1. View Hint View Answer Discuss in Forum

    m =
    cosα
    		; n =
    cosα
    cosβsinβ

    ∴ (m² + n²) cos²b
    =
    cos²α
    		 +
    cos²α
    		cos²β
    cos²βsin²β

    = cos²α
    1
    		 +
    1
    		cos²β
    cos²βsin²β

    = cos²α.cos²β
    sin²β + cos²β
    		cos²β
    cos²βsin²β.cos²β

    =
    cos²α
    		 = n²
    sin²β

    Correct Option: A

    m =
    cosα
    		; n =
    cosα
    cosβsinβ

    ∴ (m² + n²) cos²b
    =
    cos²α
    		 +
    cos²α
    		cos²β
    cos²βsin²β

    = cos²α
    1
    		 +
    1
    		cos²β
    cos²βsin²β

    = cos²α.cos²β
    sin²β + cos²β
    		cos²β
    cos²βsin²β.cos²β

    =
    cos²α
    		 = n²
    sin²β

  1. The value of tan 315° cot (–405°) is equal to








  1. View Hint View Answer Discuss in Forum

    tan 315° . cot (–405°)
    = –tan 315° . cot 405° [cot (–θ) = – cotθ]
    = – tan (360° – 45°) . cot (360° + 45°) = – (–tan 45°) . cot 45°
    = tan 45° . cot 45° = 1

    Correct Option: B

    tan 315° . cot (–405°)
    = –tan 315° . cot 405° [cot (–θ) = – cotθ]
    = – tan (360° – 45°) . cot (360° + 45°) = – (–tan 45°) . cot 45°
    = tan 45° . cot 45° = 1