If (\sin x+\cos x=\frac{3}{2}), what is the value of ((\sin x-\cos x)^2)?

Question

Answer and explanation

Correct answer: (\frac{7}{4})

First, ((\sin x+\cos x)^2=1+2\sin x\cos x) gives (\sin x\cos x=\frac{5}{8}). Then ((\sin x-\cos x)^2=1-2\sin x\cos x=\frac{7}{4}).

What is the correct answer to this question?

(\frac{7}{4})

Why is this the correct answer?

First, ((\sin x+\cos x)^2=1+2\sin x\cos x) gives (\sin x\cos x=\frac{5}{8}). Then ((\sin x-\cos x)^2=1-2\sin x\cos x=\frac{7}{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.