Trigonometry
Trigonometric Identities, Compound Angles
jee_main_2026_april_4_shift_2
Grade 12
Question:
If cos θ = 3/5 and θ is acute, and tan φ = 3/4 where φ is acute, find the value of sin(θ + φ).
A. 1
B. 7/25
C. 24/25
D. 4/5
Step-by-Step Solution
Key Concept: Find sin θ and cos φ, sin φ using Pythagorean identities, then use sin(A+B) formula.
Step 1: cos θ = 3/5 => sin θ = 4/5. Step 2: tan φ = 3/4 => sin φ = 3/5, cos φ = 4/5. Step 3: sin(θ+φ) = sin θ cos φ + cos θ sin φ = (4/5)(4/5) + (3/5)(3/5) = 16/25 + 9/25 = 25/25 = 1.
Correct Answer: A
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