What is the maximum value of \(\sin \theta+\cos \theta\)?
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Answer and explanation
Correct answer: \(\sqrt{2}\)
\( \sin \theta+\cos \theta=\sqrt{2}\sin\left(\theta+\frac{\pi}{4}\right)\), so the maximum is \( \sqrt{2}\). In exams use maximum of (a\sin x+b\cos x) as \( \sqrt{a^2+b^2}\).
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{2}\)
Why is this the correct answer?
\( \sin \theta+\cos \theta=\sqrt{2}\sin\left(\theta+\frac{\pi}{4}\right)\), so the maximum is \( \sqrt{2}\). In exams use maximum of (a\sin x+b\cos x) as \( \sqrt{a^2+b^2}\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
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