Trigonometric Identities Quiz
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Questions and Answers

What is the value of cosec A - sec A?

  • cos A - sin A
  • 1 (correct)
  • sin A/cos A
  • cos A + sin A

    • If a cos θ + b sin θ = m and a sin θ − b cos θ = n, what is the value of a^2 + b^2?

  • m^2 + n^2 (correct)
  • m^2 + n^2 + 2mn
  • m^2 - n^2
  • m^2 - n^2 + 2mn

    • What is the value of tan A + cot A?

  • 2
  • 1
  • 2cosec A (correct)
  • sec A + cosec A

    • What is the value of cos A + cos^2 A, if cos A + cos^2 A = 1?

    <p>1/2</p> Signup and view all the answers

    If cosec θ = 2x and cot θ = 1/2, what is the value of x?

    <p>1/2</p> Signup and view all the answers

    What is the value of sin^2 θ + cos^2 θ, if sin θ + cos θ = 1?

    <p>1</p> Signup and view all the answers

    What is the value of (1 + cot A + tan A)(sin A - cos A)?

    <p>sin A tan A - cot A cos A</p> Signup and view all the answers

    If sec A + tan A - 1 = 2 tan A, what is the value of sec A - tan A + 1?

    <p>2/tan A</p> Signup and view all the answers

    What is the value of (sin θ + cos θ)(tan θ + cot θ)?

    <p>sec θ + cosec θ</p> Signup and view all the answers

    If cosec θ + cot θ = m and cosec θ - cot θ = n, what is the value of mn?

    <p>1</p> Signup and view all the answers

    What is the value of 1 + cos θ + sin θ, if 1 + cos θ + sin θ = 1?

    <p>1</p> Signup and view all the answers

    What is the value of tan θ + cot θ, if tan θ + cot θ = 2?

    <p>2</p> Signup and view all the answers

    If 1 + cot A - cosec A = 2, what is the value of 1 + tan A + sec A?

    <p>2</p> Signup and view all the answers

    What is the value of sec θ cosec θ - 2sin θ cos θ?

    <p>1</p> Signup and view all the answers

    What is the value of tan² θ + cot² θ?

    <p>sec² θ + cosec² θ</p> Signup and view all the answers

    What is the value of tan θ + 1/cos θ, if tan θ + 1/cos θ = 2?

    <p>1 + sin θ</p> Signup and view all the answers

    Study Notes

    Trigonometric Identities

    • Prove that a + b = m + n if a cos θ + b sin θ = m and a sin θ - b cos θ = n.

    Trigonometric Identities

    • Prove that sin 2A + sin 4A = 1 if cos A + cos² A = 1.

    Trigonometric Identities

    • Prove that tan θ + (1 + sin² θ) / (cos θ) = 2 / (1 - sin θ).

    Trigonometric Identities

    • (sin θ + cos θ) (tan θ + cot θ) = sec θ + cosec θ.

    Trigonometric Identities

    • (sec A + tan A - 1) (sec A - tan A + 1) = 2 tan A.

    Trigonometric Identities

    • (1 + cot A - cosec A) (1 + tan A + sec A) = 2.

    Trigonometric Identities

    • 1 / (sec A + tan A) - 1 / (sec A - tan A) = cos A cosec A - sin A sec A.

    Trigonometric Identities

    • tan A - 1 / (tan A) = 2 cosec A.

    Trigonometric Identities

    • tan A + 1 / (tan A) = sin A cos A.

    Trigonometric Identities

    • 1 + tan² A = 1 + cot² A.

    Trigonometric Identities

    • If cosec θ = 2x and cot θ = 1 / x, then x = 1 / √2.

    Trigonometric Identities

    • (1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A.

    Trigonometric Identities

    • If cosec θ + cot θ = m and cosec θ - cot θ = n, then mn = 1.

    Trigonometric Identities

    • tan θ + cot θ = 2 implies tan² θ + cot² θ = 2.

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    Trigonometry Practice Sheet (Level 2) UDAAN 2025 PDF

    Description

    Test your knowledge of trigonometric identities with these 5 problems. Prove various identities involving sine, cosine, and tangent functions.

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