Trigonometry
Trigonometric Identities, Compound Angles
jee_main_2026_april_4_shift_2
Grade 12
Question:
If tan θ = 3/4 and θ is acute, and sin φ = 5/13 where φ is acute, find the value of cos(θ - φ).
Step-by-Step Solution
Key Concept: Find sin θ, cos θ from tan θ; find cos φ from sin φ; then use cos(A-B) formula.
Step 1: tan θ = 3/4 => sin θ = 3/5, cos θ = 4/5. Step 2: sin φ = 5/13 => cos φ = 12/13. Step 3: cos(θ-φ) = cos θ cos φ + sin θ sin φ = (4/5)(12/13) + (3/5)(5/13) = 48/65 + 15/65 = 63/65.
Correct Answer: 63/65
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