If \(\sin x+\cos x=\sqrt{2}\), what is (x) in \(0\leq x<2\pi\)?

We use \(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\). The maximum \(\sqrt{2}\) occurs at \(x=\frac{\pi}{4}\).

This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.

Question

Answer and explanation

Correct answer: \( \frac{\pi}{4} \)

We use \(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\). The maximum \(\sqrt{2}\) occurs at \(x=\frac{\pi}{4}\).

What is the correct answer to this question?

\( \frac{\pi}{4} \)

Why is this the correct answer?

We use \(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\). The maximum \(\sqrt{2}\) occurs at \(x=\frac{\pi}{4}\).

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.