What is bull the difference between the greatest value and the least value of cos2 0 3 sin2 0 2...........

Quantitative Aptitude (CDS) Trignometry

What is• the difference between the greatest value and the least value of cos² 0 + 3 sin² 0 + 2?

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2024 CDS -1 MATH

- We have the expression \(\cos^2 \theta + 3 \sin^2 \theta + 2\).

- Recall that \(\cos^2 \theta + \sin^2 \theta = 1\).

- Substitute: \(\sin^2 \theta = 1 - \cos^2 \theta\).

- The expression becomes: \(\cos^2 \theta + 3(1 - \cos^2 \theta) + 2\).

- Simplified: \(-2\cos^2 \theta + 3 + 2 = -2\cos^2 \theta + 5\).

- The values of \(\cos^2 \theta\) range from 0 to 1.

- Maximum when \(\cos^2 \theta = 0\): \(-2(0) + 5 = 5\).

- Minimum when \(\cos^2 \theta = 1\): \(-2(1) + 5 = 3\).

- Difference: \(5 - 3 = 2\).

Correct Answer: Option 3, 2

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