Skip to content

Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Class 12 Mathematics Trigonometric Functions Trigonometric functions and their propertiesHardLevel 70

What is the range of \(f(x)=\sin x+\cos x\)?

Answer and explanation

Correct answer: \( [-\sqrt{2},\sqrt{2}] \)

We have \(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\). Hence the range is \( [-\sqrt{2},\sqrt{2}] \).

Tags

trigonometric-functionsrangetransformation

Frequently asked questions

What is the correct answer to this question?

\( [-\sqrt{2},\sqrt{2}] \)

Why is this the correct answer?

We have \(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\). Hence the range is \( [-\sqrt{2},\sqrt{2}] \).

Which subject and chapter does this question cover?

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

Report question