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Indian Coast Guard Navik (GD) Trigonometric Identities — practice questions

Explore 2 free Trigonometric Identities questions in Indian Coast Guard Navik (GD) Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometric Identities questions and exercises with answers

Showing questions 1–2 of 2.

If cot⁴θ + cot²θ = 2.2, then csc⁴θ − csc²θ = ?Read the answer and worked solution →If sec^4(theta) - sec^2(theta) = 3, then the value of tan^4(theta) + tan^2(theta) is:Read the answer and worked solution →

Worked practice questions

If cot⁴θ + cot²θ = 2.2, then csc⁴θ − csc²θ = ?

  1. 0
  2. 1.1
  3. 2.2
  4. 3.3
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Correct answer: C. 2.2

1. Use csc²θ = 1 + cot²θ. 2. csc⁴θ − csc²θ = csc²θ(csc²θ − 1) = (1 + cot²θ)(cot²θ). 3. Expanding: cot²θ + cot⁴θ = cot⁴θ + cot²θ = 2.2. _Source: RRB Group D CEN-02/2018 PYQ, Q.10._

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If sec^4(theta) - sec^2(theta) = 3, then the value of tan^4(theta) + tan^2(theta) is:

  1. 8
  2. 3
  3. 4
  4. 6
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Correct answer: B. 3

1. Let s = sec^2(theta) = 1 + tan^2(theta). Then s^2 - s = s(s - 1) = 3. 2. Here s - 1 = tan^2(theta), so s(s-1) = (1 + tan^2)(tan^2) = tan^2 + tan^4. 3. Thus tan^4(theta) + tan^2(theta) = 3. _Source: RRB Group D CEN-02/2018 PYQ, Q.57._

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