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NDA 2016 Maths · Mathematics · Trigonometric Functions and Identities · medium

The least value of 4sin ^2θ+9cos ^2θ is

Single correct option

The least value of 4sin⁡2θ+9cos⁡2θ4\sin^2\theta+9\cos^2\theta is
  1. A. 99
  2. B. 1313
  3. C. 44
  4. D. 66
Show answer and solution

Answer: (C) 44

Write the expression as 4sin⁡2θ+9cos⁡2θ=4+5cos⁡2θ4\sin^2\theta+9\cos^2\theta=4+5\cos^2\theta. Since cos⁡2θ≥0\cos^2\theta\ge0, the least value is 44, attained when cos⁡θ=0\cos\theta=0. The largest value is 99. The number 1313 is the sum of the coefficients and is never attained.
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Original question written in the NDA 2016 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