Question types

Trigonometric Equations question types

87 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

87
Questions
5
Question groups
5
Question types
Sample Questions

Trigonometric Equations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
The smallest value of x satisfying the equation $\sqrt{3}(\cot\text{x}+\tan\text{x})=4$ is:
  • A
    $\frac{2\pi}{3}$
  • B
    $\frac{\pi}{3}$
  • $\frac{\pi}{6}$
  • D
    $\frac{\pi}{12}$

Answer: C.

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Q 2MCQ1 Mark
General solution of $\tan5\text{x}=\cot2\text{x}$ is:
  • A
    $\frac{\text{n}\pi}{7}+\frac{\pi}{2},\ \text{n}\in\text{Z}$
  • B
    $\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{3},\ \text{n}\in\text{Z}$
  • $\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{14},\ \text{n}\in\text{Z}$
  • D
    $\text{x}=\frac{\text{n}\pi}{7}=\frac{\pi}{14},\ \text{n}\in\text{Z}$

Answer: C.

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Q 3MCQ1 Mark
The general value of x satisfying the equation $\sqrt{3}\sin\text{x}+\cos\text{x}=\sqrt{3}$ is given by:
  • A
    $\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{4}+\frac{\pi}{3},\ \text{n}\in\text{Z}$
  • $\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{3}-\frac{\pi}{6},\text{n}\in\text{Z}$
  • C
    $\text{x}=\text{n}\pi\pm\frac{\pi}{6},\ \text{n}\in\text{Z}$
  • D
    $\text{x}=\text{n}\pi\pm\frac{\pi}{3},\ \text{n}\in\text{Z}$

Answer: B.

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Q 4MCQ1 Mark
If $\cos\text{x}+\sqrt{3}\sin\text{x}=2,\text{then}\ \text{x}=$
  • $\frac{\pi}{3}$
  • B
    $\frac{2\pi}{3}$
  • C
    $\frac{4\pi}{3}$
  • D
    $\frac{5\pi}{3}$

Answer: A.

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Q 5MCQ1 Mark
If $\cot\text{x}-\tan\text{x}=\sec\text{x},$ then, x is equal to:
  • A
    $2\text{n}\pi+\frac{3\pi}{2},\text{n}\in\text{Z}$
  • $\text{n}\pi+(-1)^\text{n}\frac{\pi}{6},\text{n}\in\text{Z}$
  • C
    $\text{n}\pi+\frac{\pi}{2},\text{n}\in\text{Z}$
  • D
    None of these.

Answer: B.

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