JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
The least value of \( (cos^{2}\theta-6sin\theta~cos\theta+3~sin^{2}\theta+2) \) is:
- A -1
- B \( 4+\sqrt{10} \)
- C \( 4-\sqrt{10} \)
- D 1
Answer & Solution
Correct Answer
(C) \( 4-\sqrt{10} \)
Step-by-step Solution
Detailed explanation
\( f(\theta)=\frac{1+cos 2\theta}{2}-3~sin 2\theta+3(\frac{1-cos 2\theta}{2})+2 \) \( f(\theta)=4-3~sin 2\theta-cos 2\theta \) \(f(\theta) \in[4-\sqrt{10}, 4+\sqrt{10}]\)
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