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TS EAMCET · Maths · Trigonometric Ratios & Identities

The ratio of the maximum and minimum values attained by the function \(f(x)=1+2 \sin x+3 \cos ^2 x, 0 \leq x \leq \frac{2 \pi}{3}\) is

  1. A 3 : 1
  2. B 13 : 9
  3. C 9 : 4
  4. D 8 : 13
Verified Solution

Answer & Solution

Correct Answer

(B) 13 : 9

Step-by-step Solution

Detailed explanation

Given, \(\begin{aligned} & f(x)=1+2 \sin x+3 \cos ^2 x \\ & f(x)=1+2 \sin x+3-3 \sin ^2 x \\ & f(x)=4-3\left(\sin ^2 x-\frac{2}{3} \sin x+\frac{1}{9}\right)+\frac{1}{3} \end{aligned}\) \(f(x)=\frac{13}{3}-3\left(\sin x-\frac{1}{3}\right)^2\)…