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MHT-CET Trigonometry - II — practice questions

Explore 40 free Trigonometry - II questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometry - II questions and exercises with answers

Showing questions 1–30 of 40.

Which identity gives cos(A − B) for any two angles A and B?Read the answer and worked solution →The expansion of cos(A + B) for any angles A and B isRead the answer and worked solution →For any angles A and B, sin(A + B) equalsRead the answer and worked solution →The expansion of tan(A − B) isRead the answer and worked solution →Writing 75° as 45° + 30°, the value of sin 75° comes out asRead the answer and worked solution →Evaluate sin 40° cos 20° + cos 40° sin 20°.Read the answer and worked solution →Evaluate tan 25° + tan 20° + tan 25° tan 20°.Read the answer and worked solution →What does the double angle formula give for sin 2θ?Read the answer and worked solution →Which of these is NOT a valid form of cos 2θ?Read the answer and worked solution →Expressing tan 2θ through tanθ alone yieldsRead the answer and worked solution →The ratio sin 2θ can be written in terms of tanθ asRead the answer and worked solution →A ramp angle θ is acute with sinθ = 3/5. Find sin 2θ.Read the answer and worked solution →For acute θ with sinθ = 3/5, the quantity 1 − 2sin²θ has valueRead the answer and worked solution →Angles like θ/2 and 3θ/2 are called what with respect to θ?Read the answer and worked solution →Expanding sin(2θ + θ) fully givesRead the answer and worked solution →Writing tan(2θ + θ) in terms of tanθ givesRead the answer and worked solution →The value of sin 3θ when sinθ = 1/2 isRead the answer and worked solution →Which identity correctly converts 2 sinA cosB into a sum?Read the answer and worked solution →Which sum or difference equals 2 cosA sinB?Read the answer and worked solution →Adding the expansions of cos(A+B) and cos(A−B) yields the productRead the answer and worked solution →Subtracting cos(A+B) from cos(A−B) yields the productRead the answer and worked solution →A sum of sines, sinC + sinD, factorises asRead the answer and worked solution →To factorise sinC − sinD, one usesRead the answer and worked solution →Factorising cosC − cosD givesRead the answer and worked solution →Formulae that express sums and differences of trigonometric ratios as products are calledRead the answer and worked solution →Evaluate sin 75° + sin 15° without a calculator.Read the answer and worked solution →The value of sin 105° + cos 105° isRead the answer and worked solution →In a triangle ABC, the angles A, B and C add up toRead the answer and worked solution →Since A + B + C = π, sin(A+B) in a triangle simplifies toRead the answer and worked solution →In any triangle ABC, cos(B + C) simplifies toRead the answer and worked solution →

Worked practice questions

Which identity gives cos(A − B) for any two angles A and B?

  1. sinA cosB + cosA sinB
  2. cosA cosB − sinA sinB
  3. cosA cosB + sinA sinB
  4. sinA cosB − cosA sinB
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Correct answer: C. cosA cosB + sinA sinB

Using the distance between two points on the unit circle, cos(A − B) works out to cosA cosB + sinA sinB.

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The expansion of cos(A + B) for any angles A and B is

  1. cosA cosB + sinA sinB
  2. sinA sinB − cosA cosB
  3. sinA cosB − cosA sinB
  4. cosA cosB − sinA sinB
Show answer and solution

Correct answer: D. cosA cosB − sinA sinB

Replacing B by −B in the cos(A − B) formula flips the sign of the sine product, giving cosA cosB − sinA sinB.

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For any angles A and B, sin(A + B) equals

  1. sinA sinB + cosA cosB
  2. sinA cosB − cosA sinB
  3. sinA cosB + cosA sinB
  4. cosA cosB − sinA sinB
Show answer and solution

Correct answer: C. sinA cosB + cosA sinB

The sum formula for sine adds the two cross products, sinA cosB and cosA sinB.

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More Mathematics topics

Permutations and CombinationsProbabilityApplication of DerivativesLinear ProgrammingDifferential EquationsVectorsDefinite IntegrationMatrices