If (\sin x+\cos x=\sqrt{2}), what is the value of (\sin x\cos x)?

Question

Answer and explanation

Correct answer: (\frac{1}{2})

Squaring both sides gives (1+2\sin x\cos x=2). Hence (\sin x\cos x=\frac{1}{2}); squaring is useful in such questions.

What is the correct answer to this question?

(\frac{1}{2})

Why is this the correct answer?

Squaring both sides gives (1+2\sin x\cos x=2). Hence (\sin x\cos x=\frac{1}{2}); squaring is useful in such questions.

Which subject and chapter does this question cover?

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