Ratios, identities, complementary anglesPractice Questions & MCQs
Practice Ratios, identities, complementary angles questions from Introduction to Trigonometry (Class 10 Maths) - important MCQs with answers and step-by-step solutions. Solve the sample questions below, then practice the full set free on the RankByte app.
Ratios, identities, complementary anglesQuiz - Solve & Score
Q1. If sin θ = 3/5 and θ is acute, then (1 − tan θ)/(1 + tan θ) equals:
- A.1/7
- B.1/3
- C.7/25
- D.5/7
Answer: A. 1/7
From the stem we have: 3; 5; 1; 1. The unknown asked is: the unknown asked in the stem. Governing law - tan θ = 3/4. This is the equation that links the given quantities to the unknown (math, chapter 'Introduction to Trigonometry'). Substituting: tan θ = 3/4 → (1 − 3/4)/(1 + 3/4) = (1/4)/(7/4) = 1/7. Therefore the answer is A) 1/7.
Q2. If tan θ + 1/tan θ = 2 sec θ, then sin θ equals (θ in (0, π/2)):
- A.1/2
- B.1
- C.√3/2
- D.0
Answer: A. 1/2
Q3. If cos²θ + cos²(60° − θ) + cos²(60° + θ) = k, then k equals:
- A.3/2
- B.1
- C.2
- D.1/2
Answer: A. 3/2
Data from the problem: 60 °. Required: the unknown asked in the stem. Governing law - Using 2 cos²x = 1 + cos 2x: sum = (3 + cos 2θ + cos(120° − 2θ) + cos(120° + 2θ))/2. This is the equation that links the given quantities to the unknown (math, chapter 'Introduction to Trigonometry'). Substituting: Using 2 cos²x = 1 + cos 2x: sum = (3 + cos 2θ + cos(120° − 2θ) + cos(120° + 2θ))/2 → The sum of three cosines equally spaced at 120° apart is 0, so sum = 3/2. So the answer is A) 3/2.
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