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NDA 2020 Maths · Mathematics · Trigonometric Functions and Identities · medium

The maximum value of sin θ+cos θ is √2. 2. The minimum value of 3sin ^2θ+4cos ^2θ is 3.

Single correct option

Consider the following statements:
1. The maximum value of sin⁡θ+cos⁡θ\sin\theta+\cos\theta is 2\sqrt2.
2. The minimum value of 3sin⁡2θ+4cos⁡2θ3\sin^2\theta+4\cos^2\theta is 3.
Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (C) Both 1 and 2

sin⁡θ+cos⁡θ=2sin⁡(θ+45∘)\sin\theta+\cos\theta=\sqrt2\sin(\theta+45^\circ) has maximum 2\sqrt2. Also 3sin⁡2θ+4cos⁡2θ=3+cos⁡2θ3\sin^2\theta+4\cos^2\theta=3+\cos^2\theta, which lies between 3 and 4. So the minimum is 3 and both statements are correct.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake