NDA 2025 · PYQ · Trigonometry · easy
Let 2sinα + cosα = 2, where 0 < α < 90°. What is tanα equal to?
- A.1/2
- B.1
- C.3/4✓ Correct
- D.2
From 2sinα + cosα = 2: 2sinα = 2 - cosα. Squaring: 4sin²α = 4 - 4cosα + cos²α, so 4(1-cos²α) = 4 - 4cosα + cos²α, giving 4 - 4cos²α = 4 - 4cosα + cos²α, so 5cos²α = 4cosα, cosα = 4/5. Then sinα = 3/5, and tanα = 3/4.
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