Home » Aptitude » Trigonometry » Question

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. Find the value of tan θ(1 + sec2θ)(1 + sec 4θ) (1 + sec8θ).
    1. tan 10θ
    2. tan8θ
    3. tan 12θ
    4. 1
Correct Option: B

tan θ(1 + sec2θ)(1 + sec 4θ) (1 + sec8θ) = tanθ 1 +
1
 1 +
1
 1 +
1
cos2θcos4θcos8θ

tan θ(1 + sec2θ)(1 + sec 4θ) (1 + sec8θ) = tanθ
cos2θ + 1
cos4θ + 1
cos8θ + 1
cos2θcos4θcos8θ

tan θ(1 + sec2θ)(1 + sec 4θ) (1 + sec8θ) = tanθ
2cos2θ
2cos22θ
2cos24θ
cos2θcos4θcos8θ

[ ∴ 1 + cos2θ = 2cos2θ ]
Required answer = 8 .
tanθ.cos2θ .cos2θ.cos4θ
cos8θ

Required answer = 4 .
2sinθcosθ.cos2θ.cos4θ
cos8θ

Required answer = 4 .
sin2θ.cos2θ.cos4θ
cos8θ

Required answer = 2 .
2sin2θ.cos2θ.cos4θ
cos8θ

Required answer =
2sin4θ.cos4θ
cos8θ

Required answer =
sin8θ
 = tan8θ
cos8θ


Your comments will be displayed only after manual approval.