NDA 2024 · PYQ · Trigonometry · medium
What is (√3 cos10° – sin10°)/(sin25° cos25°) equal to?
Answer
The correct answer is D: 4. √3 cos10° – sin10° = 2(cos30°cos10° – sin30°sin10°) = 2cos(30°+10°) = 2cos40° = 2sin50°. Denominator: sin25°cos25° = (1/2)sin50°.
- A.1
- B.√3
- C.2
- D.4✓ Correct
√3 cos10° – sin10° = 2(cos30°cos10° – sin30°sin10°) = 2cos(30°+10°) = 2cos40° = 2sin50°. Denominator: sin25°cos25° = (1/2)sin50°. So the expression = 2sin50°/[(1/2)sin50°] = 4.
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