Trigonometry
Trigonometric Ratios, Standard Angles
jee_main_2026_april_6_shift_2
Grade None
Question:
If cos 60° × tan 45° = a and sin 30° × cot 60° = b, find a + b.
A. (1+√3)/2
B. (1+2√3)/3
C. (3+√3)/6
D. (6+√3)/12
Step-by-Step Solution
Key Concept: Use standard trigonometric values.
Step 1: cos 60° × tan 45° = (1/2) × 1 = 1/2. So a = 1/2. Step 2: sin 30° × cot 60° = (1/2) × (1/√3) = 1/(2√3). So b = 1/(2√3). Step 3: a + b = 1/2 + 1/(2√3) = (√3 + 1)/(2√3) = (3 + √3)/6.
Correct Answer: C
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