SSC CHSL 2025 · PYQ · Trigonometry · medium
If 2sin²A + 2√2 cosA − 3 = 0, then find the value of tan A.
Answer
The correct answer is D: 1. Substituting 2sin²A = 2(1-cos²A): 2-2cos²A+2√2 cosA-3=0 → -2cos²A+2√2 cosA-1=0 → 2cos²A-2√2 cosA+1=0. Using quadratic formula: cosA = (2√2 ± √(8-8))/4 = 2√2/4 = √2/2, so A=45° and tanA=1.
- A.√2
- B.0
- C.1√2
- D.1✓ Correct
Substituting 2sin²A = 2(1-cos²A): 2-2cos²A+2√2 cosA-3=0 → -2cos²A+2√2 cosA-1=0 → 2cos²A-2√2 cosA+1=0. Using quadratic formula: cosA = (2√2 ± √(8-8))/4 = 2√2/4 = √2/2, so A=45° and tanA=1.
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